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Why doesn't current pass through a resistance if there is another path without resistance?
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Why doesn't current pass through a resistance if there is another path without resistance? How does it know there is resistance on that path ?
electric-circuits electric-current electrical-resistance
edited 1 hour ago
Qmechanic♦
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asked 1 hour ago
ten1o
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Why doesn't current pass through a resistance if there is another path without resistance? How does it know there is resistance on that path ?
electric-circuits electric-current electrical-resistance
edited 1 hour ago
Qmechanic♦
98.5k121741075
asked 1 hour ago
ten1o
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It's the same logic as how water flows via the easiest path. In the case of electricity, it minimizes the energetic cost. It is a very general principle.
– Peter Diehr
1 hour ago
@PeterDiehr Does the "force" potential difference field of the battery travel faster than the charge?
– ten1o
1 hour ago
Related: physics.stackexchange.com/q/188371/2451
– Qmechanic♦
1 hour ago
The potential difference is a field effect, and travels at nearly the speed of light; the actual electron motion is very slow, as measured by the drift velocity, which is super-imposed upon the much greater, but random, thermal velocity of the free electrons. As a result, the field effects (the emf) travels much faster than the effective current.
– Peter Diehr
1 hour ago
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
Why doesn't current pass through a resistance if there is another path without resistance? How does it know there is resistance on that path ?
electric-circuits electric-current electrical-resistance
edited 1 hour ago
Qmechanic♦
98.5k121741075
asked 1 hour ago
ten1o
213
Why doesn't current pass through a resistance if there is another path without resistance? How does it know there is resistance on that path ?
electric-circuits electric-current electrical-resistance
electric-circuits electric-current electrical-resistance
edited 1 hour ago
Qmechanic♦
98.5k121741075
asked 1 hour ago
ten1o
213
edited 1 hour ago
Qmechanic♦
98.5k121741075
asked 1 hour ago
ten1o
213
edited 1 hour ago
Qmechanic♦
98.5k121741075
edited 1 hour ago
Qmechanic♦
98.5k121741075
edited 1 hour ago
Qmechanic♦
98.5k121741075
98.5k121741075
asked 1 hour ago
ten1o
213
asked 1 hour ago
ten1o
213
asked 1 hour ago
ten1o
213
213
1
It's the same logic as how water flows via the easiest path. In the case of electricity, it minimizes the energetic cost. It is a very general principle.
– Peter Diehr
1 hour ago
@PeterDiehr Does the "force" potential difference field of the battery travel faster than the charge?
– ten1o
1 hour ago
Related: physics.stackexchange.com/q/188371/2451
– Qmechanic♦
1 hour ago
The potential difference is a field effect, and travels at nearly the speed of light; the actual electron motion is very slow, as measured by the drift velocity, which is super-imposed upon the much greater, but random, thermal velocity of the free electrons. As a result, the field effects (the emf) travels much faster than the effective current.
– Peter Diehr
1 hour ago
add a comment |Â
1
It's the same logic as how water flows via the easiest path. In the case of electricity, it minimizes the energetic cost. It is a very general principle.
– Peter Diehr
1 hour ago
@PeterDiehr Does the "force" potential difference field of the battery travel faster than the charge?
– ten1o
1 hour ago
Related: physics.stackexchange.com/q/188371/2451
– Qmechanic♦
1 hour ago
The potential difference is a field effect, and travels at nearly the speed of light; the actual electron motion is very slow, as measured by the drift velocity, which is super-imposed upon the much greater, but random, thermal velocity of the free electrons. As a result, the field effects (the emf) travels much faster than the effective current.
– Peter Diehr
1 hour ago
1
1
It's the same logic as how water flows via the easiest path. In the case of electricity, it minimizes the energetic cost. It is a very general principle.
– Peter Diehr
1 hour ago
It's the same logic as how water flows via the easiest path. In the case of electricity, it minimizes the energetic cost. It is a very general principle.
– Peter Diehr
1 hour ago
@PeterDiehr Does the "force" potential difference field of the battery travel faster than the charge?
– ten1o
1 hour ago
@PeterDiehr Does the "force" potential difference field of the battery travel faster than the charge?
– ten1o
1 hour ago
Related: physics.stackexchange.com/q/188371/2451
– Qmechanic♦
1 hour ago
Related: physics.stackexchange.com/q/188371/2451
– Qmechanic♦
1 hour ago
The potential difference is a field effect, and travels at nearly the speed of light; the actual electron motion is very slow, as measured by the drift velocity, which is super-imposed upon the much greater, but random, thermal velocity of the free electrons. As a result, the field effects (the emf) travels much faster than the effective current.
– Peter Diehr
1 hour ago
The potential difference is a field effect, and travels at nearly the speed of light; the actual electron motion is very slow, as measured by the drift velocity, which is super-imposed upon the much greater, but random, thermal velocity of the free electrons. As a result, the field effects (the emf) travels much faster than the effective current.
– Peter Diehr
1 hour ago
add a comment |Â
4 Answers
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up vote
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If there is a parallel path without resistance then the voltage across the terminals is zero. If the voltage is zero then, by Ohm’s law, the current through any branch with resistance is also zero.
answered 1 hour ago
Dale
2,486415
add a comment |Â
up vote
1
down vote
The basic circuit theory "rules" you imply, are high level simplifications applicable at a large scale and at slow speeds.
If you look at it close and fast enough, you could say that a current really starts to go into the obstructed path, but the electric field in front of the obstruction would build up gradually and current will start to repartition into the free path where it can start to flow. Naively you could say that the electric field will "sniff out" the paths. Actually in reality the current will also bounce off the obstructions, reflect and go back and forth etc. This is a real mess in practical electrical engineering at high frequencies.
answered 44 mins ago
BjornW
5,35011925
add a comment |Â
up vote
1
down vote
Why doesn't current pass through a resistance if there is another path
without resistance?
Stipulate that there are two parallel connected resistors with resistance $R_1$ and $R_2$ respectively.
Since they are parallel connected, the current $I$ into the resistor network divides according to current division:
$$I_1 = IfracR_2R_1 + R_2$$
$$I_2 = IfracR_1R_1 + R_2$$
Now, let the resistance $R_2$ go to zero while holding $R_1$ fixed and see that, as $R_2$ gets smaller, the current through $R_1$ gets smaller and that, when $R_2 = 0$
$$I_1 = I frac0R_1 + 0 = 0$$
$$I_2 = I fracR_1R_1 + 0 = I$$
answered 36 mins ago
Alfred Centauri
46.2k344138
add a comment |Â
up vote
0
down vote
An electric charge will experience a force if an electric field is applied. If it is free to move, it will thus move contributing to a current. This is what the basic idea of 'Electric Currents in Conductors' is and this is apparently known to you. In nature, free charged particles do exist like in upper strata of atmosphere called the ionosphere. However, in atoms and molecules, the negatively charged electrons and the positively charged nuclei are bound to each other and are thus not free to move. Bulk matter is made up of many molecules a gram of water, for example, contains approximately $ 10^22 $ molecules. These molecules are so closely packed that the electrons are no longer attached to individual nuclei. In some materials the electrons will still be bound, i.e., they will not accelerate even if an electric field is applied. In other materials, notably metals, according to the Drude-Lorentz Electron-sea theory, some electrons are practically free to move within the bulk material.
Resistance to electircal flow is due to the fact that when charge is given to a resistance, it remains stationary. In case of conductor, it is delocalised so it gets displaced and spread evenly on the surface, so NOTE THIS CAREFULLY: IN A CONDUCTOR, CHARGE FLOWS MOSTLY ON THE SURFACE ITSELF. This requires, undoubtedly some potential difference accross the ends of the conductor but very less in magnitude. So, another fundamental rule/observation of universe is that "ANY DYNAMICAL PROCESS OCCURS IN THE PATH THAT REQUIRES LEAST ENERGY EXPENSE".
The most general and fundamental formula for Joule heating is:
$$ displaystyle P=(V_A-V_B)I $$
where
$P$ is the power (energy per unit time) converted from electrical energy to thermal energy,
$I$ is the current travelling through the resistor or other element,
$displaystyle V_A-V_B$ is the voltage drop across the element.
The explanation of this formula (P=VI) is:
(Energy dissipated per unit time) = (Energy dissipated per charge passing through resistor) × (Charge passing through resistor per unit time)
When Ohm's law is also applicable, the formula can be written in other equivalent forms:
$$displaystyle P=IV=I^2R=V^2/R$$
When current varies, as it does in AC circuits,
$$displaystyle P(t)=U(t)I(t)$$
where $t$ is time and $P$ is the instantaneous power being converted from electrical energy to heat. Far more often, the average power is of more interest than the instantaneous power:
$$displaystyle P_avg=U_textrmsI_textrms=I_textrms^2R=U_textrms^2/R$$
where "avg" denotes average (mean) over one or more cycles, and "rms" denotes root mean square.
These formulas are valid for an ideal resistor, with zero reactance. If the reactance is nonzero, the formulas are modified:$$displaystyle P_avg=U_textrmsI_textrmscos phi =I_textrms^2operatorname Re (Z)=U_textrms^2operatorname Re (Y^*)$$
where $phi$ is the phase difference between current and voltage,$Re$ means real part, $Z$ is the complex impedance, and Y* is the complex conjugate of the admittance (equal to $1/Z*$).
So, this shows how energy inefficient is electric flow through a resistance under an applied potential.
answered 42 mins ago
Vishnurochishnu Sahishnu
1
New contributor
Vishnurochishnu Sahishnu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
If there is a parallel path without resistance then the voltage across the terminals is zero. If the voltage is zero then, by Ohm’s law, the current through any branch with resistance is also zero.
answered 1 hour ago
Dale
2,486415
add a comment |Â
up vote
1
down vote
If there is a parallel path without resistance then the voltage across the terminals is zero. If the voltage is zero then, by Ohm’s law, the current through any branch with resistance is also zero.
answered 1 hour ago
Dale
2,486415
add a comment |Â
up vote
1
down vote
up vote
1
down vote
If there is a parallel path without resistance then the voltage across the terminals is zero. If the voltage is zero then, by Ohm’s law, the current through any branch with resistance is also zero.
answered 1 hour ago
Dale
2,486415
If there is a parallel path without resistance then the voltage across the terminals is zero. If the voltage is zero then, by Ohm’s law, the current through any branch with resistance is also zero.
answered 1 hour ago
Dale
2,486415
answered 1 hour ago
Dale
2,486415
answered 1 hour ago
Dale
2,486415
answered 1 hour ago
Dale
2,486415
2,486415
add a comment |Â
add a comment |Â
up vote
1
down vote
The basic circuit theory "rules" you imply, are high level simplifications applicable at a large scale and at slow speeds.
If you look at it close and fast enough, you could say that a current really starts to go into the obstructed path, but the electric field in front of the obstruction would build up gradually and current will start to repartition into the free path where it can start to flow. Naively you could say that the electric field will "sniff out" the paths. Actually in reality the current will also bounce off the obstructions, reflect and go back and forth etc. This is a real mess in practical electrical engineering at high frequencies.
answered 44 mins ago
BjornW
5,35011925
add a comment |Â
up vote
1
down vote
The basic circuit theory "rules" you imply, are high level simplifications applicable at a large scale and at slow speeds.
If you look at it close and fast enough, you could say that a current really starts to go into the obstructed path, but the electric field in front of the obstruction would build up gradually and current will start to repartition into the free path where it can start to flow. Naively you could say that the electric field will "sniff out" the paths. Actually in reality the current will also bounce off the obstructions, reflect and go back and forth etc. This is a real mess in practical electrical engineering at high frequencies.
answered 44 mins ago
BjornW
5,35011925
add a comment |Â
up vote
1
down vote
up vote
1
down vote
The basic circuit theory "rules" you imply, are high level simplifications applicable at a large scale and at slow speeds.
If you look at it close and fast enough, you could say that a current really starts to go into the obstructed path, but the electric field in front of the obstruction would build up gradually and current will start to repartition into the free path where it can start to flow. Naively you could say that the electric field will "sniff out" the paths. Actually in reality the current will also bounce off the obstructions, reflect and go back and forth etc. This is a real mess in practical electrical engineering at high frequencies.
answered 44 mins ago
BjornW
5,35011925
The basic circuit theory "rules" you imply, are high level simplifications applicable at a large scale and at slow speeds.
If you look at it close and fast enough, you could say that a current really starts to go into the obstructed path, but the electric field in front of the obstruction would build up gradually and current will start to repartition into the free path where it can start to flow. Naively you could say that the electric field will "sniff out" the paths. Actually in reality the current will also bounce off the obstructions, reflect and go back and forth etc. This is a real mess in practical electrical engineering at high frequencies.
answered 44 mins ago
BjornW
5,35011925
answered 44 mins ago
BjornW
5,35011925
answered 44 mins ago
BjornW
5,35011925
answered 44 mins ago
BjornW
5,35011925
5,35011925
add a comment |Â
add a comment |Â
up vote
1
down vote
Why doesn't current pass through a resistance if there is another path
without resistance?
Stipulate that there are two parallel connected resistors with resistance $R_1$ and $R_2$ respectively.
Since they are parallel connected, the current $I$ into the resistor network divides according to current division:
$$I_1 = IfracR_2R_1 + R_2$$
$$I_2 = IfracR_1R_1 + R_2$$
Now, let the resistance $R_2$ go to zero while holding $R_1$ fixed and see that, as $R_2$ gets smaller, the current through $R_1$ gets smaller and that, when $R_2 = 0$
$$I_1 = I frac0R_1 + 0 = 0$$
$$I_2 = I fracR_1R_1 + 0 = I$$
answered 36 mins ago
Alfred Centauri
46.2k344138
add a comment |Â
up vote
1
down vote
Why doesn't current pass through a resistance if there is another path
without resistance?
Stipulate that there are two parallel connected resistors with resistance $R_1$ and $R_2$ respectively.
Since they are parallel connected, the current $I$ into the resistor network divides according to current division:
$$I_1 = IfracR_2R_1 + R_2$$
$$I_2 = IfracR_1R_1 + R_2$$
Now, let the resistance $R_2$ go to zero while holding $R_1$ fixed and see that, as $R_2$ gets smaller, the current through $R_1$ gets smaller and that, when $R_2 = 0$
$$I_1 = I frac0R_1 + 0 = 0$$
$$I_2 = I fracR_1R_1 + 0 = I$$
answered 36 mins ago
Alfred Centauri
46.2k344138
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Why doesn't current pass through a resistance if there is another path
without resistance?
Stipulate that there are two parallel connected resistors with resistance $R_1$ and $R_2$ respectively.
Since they are parallel connected, the current $I$ into the resistor network divides according to current division:
$$I_1 = IfracR_2R_1 + R_2$$
$$I_2 = IfracR_1R_1 + R_2$$
Now, let the resistance $R_2$ go to zero while holding $R_1$ fixed and see that, as $R_2$ gets smaller, the current through $R_1$ gets smaller and that, when $R_2 = 0$
$$I_1 = I frac0R_1 + 0 = 0$$
$$I_2 = I fracR_1R_1 + 0 = I$$
answered 36 mins ago
Alfred Centauri
46.2k344138
Why doesn't current pass through a resistance if there is another path
without resistance?
Stipulate that there are two parallel connected resistors with resistance $R_1$ and $R_2$ respectively.
Since they are parallel connected, the current $I$ into the resistor network divides according to current division:
$$I_1 = IfracR_2R_1 + R_2$$
$$I_2 = IfracR_1R_1 + R_2$$
Now, let the resistance $R_2$ go to zero while holding $R_1$ fixed and see that, as $R_2$ gets smaller, the current through $R_1$ gets smaller and that, when $R_2 = 0$
$$I_1 = I frac0R_1 + 0 = 0$$
$$I_2 = I fracR_1R_1 + 0 = I$$
answered 36 mins ago
Alfred Centauri
46.2k344138
answered 36 mins ago
Alfred Centauri
46.2k344138
answered 36 mins ago
Alfred Centauri
46.2k344138
answered 36 mins ago
Alfred Centauri
46.2k344138
46.2k344138
add a comment |Â
add a comment |Â
up vote
0
down vote
An electric charge will experience a force if an electric field is applied. If it is free to move, it will thus move contributing to a current. This is what the basic idea of 'Electric Currents in Conductors' is and this is apparently known to you. In nature, free charged particles do exist like in upper strata of atmosphere called the ionosphere. However, in atoms and molecules, the negatively charged electrons and the positively charged nuclei are bound to each other and are thus not free to move. Bulk matter is made up of many molecules a gram of water, for example, contains approximately $ 10^22 $ molecules. These molecules are so closely packed that the electrons are no longer attached to individual nuclei. In some materials the electrons will still be bound, i.e., they will not accelerate even if an electric field is applied. In other materials, notably metals, according to the Drude-Lorentz Electron-sea theory, some electrons are practically free to move within the bulk material.
Resistance to electircal flow is due to the fact that when charge is given to a resistance, it remains stationary. In case of conductor, it is delocalised so it gets displaced and spread evenly on the surface, so NOTE THIS CAREFULLY: IN A CONDUCTOR, CHARGE FLOWS MOSTLY ON THE SURFACE ITSELF. This requires, undoubtedly some potential difference accross the ends of the conductor but very less in magnitude. So, another fundamental rule/observation of universe is that "ANY DYNAMICAL PROCESS OCCURS IN THE PATH THAT REQUIRES LEAST ENERGY EXPENSE".
The most general and fundamental formula for Joule heating is:
$$ displaystyle P=(V_A-V_B)I $$
where
$P$ is the power (energy per unit time) converted from electrical energy to thermal energy,
$I$ is the current travelling through the resistor or other element,
$displaystyle V_A-V_B$ is the voltage drop across the element.
The explanation of this formula (P=VI) is:
(Energy dissipated per unit time) = (Energy dissipated per charge passing through resistor) × (Charge passing through resistor per unit time)
When Ohm's law is also applicable, the formula can be written in other equivalent forms:
$$displaystyle P=IV=I^2R=V^2/R$$
When current varies, as it does in AC circuits,
$$displaystyle P(t)=U(t)I(t)$$
where $t$ is time and $P$ is the instantaneous power being converted from electrical energy to heat. Far more often, the average power is of more interest than the instantaneous power:
$$displaystyle P_avg=U_textrmsI_textrms=I_textrms^2R=U_textrms^2/R$$
where "avg" denotes average (mean) over one or more cycles, and "rms" denotes root mean square.
These formulas are valid for an ideal resistor, with zero reactance. If the reactance is nonzero, the formulas are modified:$$displaystyle P_avg=U_textrmsI_textrmscos phi =I_textrms^2operatorname Re (Z)=U_textrms^2operatorname Re (Y^*)$$
where $phi$ is the phase difference between current and voltage,$Re$ means real part, $Z$ is the complex impedance, and Y* is the complex conjugate of the admittance (equal to $1/Z*$).
So, this shows how energy inefficient is electric flow through a resistance under an applied potential.
answered 42 mins ago
Vishnurochishnu Sahishnu
1
New contributor
Vishnurochishnu Sahishnu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
0
down vote
An electric charge will experience a force if an electric field is applied. If it is free to move, it will thus move contributing to a current. This is what the basic idea of 'Electric Currents in Conductors' is and this is apparently known to you. In nature, free charged particles do exist like in upper strata of atmosphere called the ionosphere. However, in atoms and molecules, the negatively charged electrons and the positively charged nuclei are bound to each other and are thus not free to move. Bulk matter is made up of many molecules a gram of water, for example, contains approximately $ 10^22 $ molecules. These molecules are so closely packed that the electrons are no longer attached to individual nuclei. In some materials the electrons will still be bound, i.e., they will not accelerate even if an electric field is applied. In other materials, notably metals, according to the Drude-Lorentz Electron-sea theory, some electrons are practically free to move within the bulk material.
Resistance to electircal flow is due to the fact that when charge is given to a resistance, it remains stationary. In case of conductor, it is delocalised so it gets displaced and spread evenly on the surface, so NOTE THIS CAREFULLY: IN A CONDUCTOR, CHARGE FLOWS MOSTLY ON THE SURFACE ITSELF. This requires, undoubtedly some potential difference accross the ends of the conductor but very less in magnitude. So, another fundamental rule/observation of universe is that "ANY DYNAMICAL PROCESS OCCURS IN THE PATH THAT REQUIRES LEAST ENERGY EXPENSE".
The most general and fundamental formula for Joule heating is:
$$ displaystyle P=(V_A-V_B)I $$
where
$P$ is the power (energy per unit time) converted from electrical energy to thermal energy,
$I$ is the current travelling through the resistor or other element,
$displaystyle V_A-V_B$ is the voltage drop across the element.
The explanation of this formula (P=VI) is:
(Energy dissipated per unit time) = (Energy dissipated per charge passing through resistor) × (Charge passing through resistor per unit time)
When Ohm's law is also applicable, the formula can be written in other equivalent forms:
$$displaystyle P=IV=I^2R=V^2/R$$
When current varies, as it does in AC circuits,
$$displaystyle P(t)=U(t)I(t)$$
where $t$ is time and $P$ is the instantaneous power being converted from electrical energy to heat. Far more often, the average power is of more interest than the instantaneous power:
$$displaystyle P_avg=U_textrmsI_textrms=I_textrms^2R=U_textrms^2/R$$
where "avg" denotes average (mean) over one or more cycles, and "rms" denotes root mean square.
These formulas are valid for an ideal resistor, with zero reactance. If the reactance is nonzero, the formulas are modified:$$displaystyle P_avg=U_textrmsI_textrmscos phi =I_textrms^2operatorname Re (Z)=U_textrms^2operatorname Re (Y^*)$$
where $phi$ is the phase difference between current and voltage,$Re$ means real part, $Z$ is the complex impedance, and Y* is the complex conjugate of the admittance (equal to $1/Z*$).
So, this shows how energy inefficient is electric flow through a resistance under an applied potential.
answered 42 mins ago
Vishnurochishnu Sahishnu
1
New contributor
Vishnurochishnu Sahishnu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
0
down vote
up vote
0
down vote
An electric charge will experience a force if an electric field is applied. If it is free to move, it will thus move contributing to a current. This is what the basic idea of 'Electric Currents in Conductors' is and this is apparently known to you. In nature, free charged particles do exist like in upper strata of atmosphere called the ionosphere. However, in atoms and molecules, the negatively charged electrons and the positively charged nuclei are bound to each other and are thus not free to move. Bulk matter is made up of many molecules a gram of water, for example, contains approximately $ 10^22 $ molecules. These molecules are so closely packed that the electrons are no longer attached to individual nuclei. In some materials the electrons will still be bound, i.e., they will not accelerate even if an electric field is applied. In other materials, notably metals, according to the Drude-Lorentz Electron-sea theory, some electrons are practically free to move within the bulk material.
Resistance to electircal flow is due to the fact that when charge is given to a resistance, it remains stationary. In case of conductor, it is delocalised so it gets displaced and spread evenly on the surface, so NOTE THIS CAREFULLY: IN A CONDUCTOR, CHARGE FLOWS MOSTLY ON THE SURFACE ITSELF. This requires, undoubtedly some potential difference accross the ends of the conductor but very less in magnitude. So, another fundamental rule/observation of universe is that "ANY DYNAMICAL PROCESS OCCURS IN THE PATH THAT REQUIRES LEAST ENERGY EXPENSE".
The most general and fundamental formula for Joule heating is:
$$ displaystyle P=(V_A-V_B)I $$
where
$P$ is the power (energy per unit time) converted from electrical energy to thermal energy,
$I$ is the current travelling through the resistor or other element,
$displaystyle V_A-V_B$ is the voltage drop across the element.
The explanation of this formula (P=VI) is:
(Energy dissipated per unit time) = (Energy dissipated per charge passing through resistor) × (Charge passing through resistor per unit time)
When Ohm's law is also applicable, the formula can be written in other equivalent forms:
$$displaystyle P=IV=I^2R=V^2/R$$
When current varies, as it does in AC circuits,
$$displaystyle P(t)=U(t)I(t)$$
where $t$ is time and $P$ is the instantaneous power being converted from electrical energy to heat. Far more often, the average power is of more interest than the instantaneous power:
$$displaystyle P_avg=U_textrmsI_textrms=I_textrms^2R=U_textrms^2/R$$
where "avg" denotes average (mean) over one or more cycles, and "rms" denotes root mean square.
These formulas are valid for an ideal resistor, with zero reactance. If the reactance is nonzero, the formulas are modified:$$displaystyle P_avg=U_textrmsI_textrmscos phi =I_textrms^2operatorname Re (Z)=U_textrms^2operatorname Re (Y^*)$$
where $phi$ is the phase difference between current and voltage,$Re$ means real part, $Z$ is the complex impedance, and Y* is the complex conjugate of the admittance (equal to $1/Z*$).
So, this shows how energy inefficient is electric flow through a resistance under an applied potential.
answered 42 mins ago
Vishnurochishnu Sahishnu
1
New contributor
Vishnurochishnu Sahishnu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
An electric charge will experience a force if an electric field is applied. If it is free to move, it will thus move contributing to a current. This is what the basic idea of 'Electric Currents in Conductors' is and this is apparently known to you. In nature, free charged particles do exist like in upper strata of atmosphere called the ionosphere. However, in atoms and molecules, the negatively charged electrons and the positively charged nuclei are bound to each other and are thus not free to move. Bulk matter is made up of many molecules a gram of water, for example, contains approximately $ 10^22 $ molecules. These molecules are so closely packed that the electrons are no longer attached to individual nuclei. In some materials the electrons will still be bound, i.e., they will not accelerate even if an electric field is applied. In other materials, notably metals, according to the Drude-Lorentz Electron-sea theory, some electrons are practically free to move within the bulk material.
Resistance to electircal flow is due to the fact that when charge is given to a resistance, it remains stationary. In case of conductor, it is delocalised so it gets displaced and spread evenly on the surface, so NOTE THIS CAREFULLY: IN A CONDUCTOR, CHARGE FLOWS MOSTLY ON THE SURFACE ITSELF. This requires, undoubtedly some potential difference accross the ends of the conductor but very less in magnitude. So, another fundamental rule/observation of universe is that "ANY DYNAMICAL PROCESS OCCURS IN THE PATH THAT REQUIRES LEAST ENERGY EXPENSE".
The most general and fundamental formula for Joule heating is:
$$ displaystyle P=(V_A-V_B)I $$
where
$P$ is the power (energy per unit time) converted from electrical energy to thermal energy,
$I$ is the current travelling through the resistor or other element,
$displaystyle V_A-V_B$ is the voltage drop across the element.
The explanation of this formula (P=VI) is:
(Energy dissipated per unit time) = (Energy dissipated per charge passing through resistor) × (Charge passing through resistor per unit time)
When Ohm's law is also applicable, the formula can be written in other equivalent forms:
$$displaystyle P=IV=I^2R=V^2/R$$
When current varies, as it does in AC circuits,
$$displaystyle P(t)=U(t)I(t)$$
where $t$ is time and $P$ is the instantaneous power being converted from electrical energy to heat. Far more often, the average power is of more interest than the instantaneous power:
$$displaystyle P_avg=U_textrmsI_textrms=I_textrms^2R=U_textrms^2/R$$
where "avg" denotes average (mean) over one or more cycles, and "rms" denotes root mean square.
These formulas are valid for an ideal resistor, with zero reactance. If the reactance is nonzero, the formulas are modified:$$displaystyle P_avg=U_textrmsI_textrmscos phi =I_textrms^2operatorname Re (Z)=U_textrms^2operatorname Re (Y^*)$$
where $phi$ is the phase difference between current and voltage,$Re$ means real part, $Z$ is the complex impedance, and Y* is the complex conjugate of the admittance (equal to $1/Z*$).
So, this shows how energy inefficient is electric flow through a resistance under an applied potential.
answered 42 mins ago
Vishnurochishnu Sahishnu
1
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Vishnurochishnu Sahishnu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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answered 42 mins ago
Vishnurochishnu Sahishnu
1
New contributor
Vishnurochishnu Sahishnu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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answered 42 mins ago
Vishnurochishnu Sahishnu
1
answered 42 mins ago
Vishnurochishnu Sahishnu
1
1
New contributor
Vishnurochishnu Sahishnu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Vishnurochishnu Sahishnu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Vishnurochishnu Sahishnu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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It's the same logic as how water flows via the easiest path. In the case of electricity, it minimizes the energetic cost. It is a very general principle.
– Peter Diehr
1 hour ago
@PeterDiehr Does the "force" potential difference field of the battery travel faster than the charge?
– ten1o
1 hour ago
Related: physics.stackexchange.com/q/188371/2451
– Qmechanic♦
1 hour ago
The potential difference is a field effect, and travels at nearly the speed of light; the actual electron motion is very slow, as measured by the drift velocity, which is super-imposed upon the much greater, but random, thermal velocity of the free electrons. As a result, the field effects (the emf) travels much faster than the effective current.
– Peter Diehr
1 hour ago