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Potential difference across inductor

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Consider the circuit shown in figure. The switch S is closed for t. < O, and steady-state conditions are established. The switch is then open ed at t = 0. Then we have to find potential difference and current through each inductor for the instant immediately after t = 0.

According to me at steady state , we can replace inductor as a simple wire .
So equivalent resistance will be 2R
And current through battery would be V/2R

As we replaced inductor with a wire so the potential difference across it should be zero .

But the answer given as 3V/2 and V for L$_1$ and L $_2$ respctively .

asked Jan 11, 2017 in Physics Problems by koolman (4,286 points)
edited Jan 12, 2017 by koolman
How do you get the resistance to be $\frac83R$? I make it $2R$.
Sorry calculation mistake . It it 2R ,but how to proceed.

1 Answer

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Best answer

The effect of an inductor is to keep the current at the same value. When the battery is disconnected after reaching the steady state, inductors $L_1$ and $L_2$ become sources of current. The voltage across each is such as to keep the same current flowing through each while ensuring that Kirchhoff's Rules are satisfied.

So the way to tackle this problem is : (1) find the currents through each inductor when the battery is connected; (2) after the battery is disconnected, imagine each inductor to be a battery of such voltage that the current through each is the same as before. The sum of the voltage drops around each of the 2 loops that remain must be zero. This enables you to find the PD across each inductor.

I agree with the answers given $(L_1=\frac32V, L_2=V)$.

It may seem wrong that voltages in the circuit can be greater than the applied voltage $V$ - or even equal to $V$ when there are resistors in the circuit. In an RC network the voltage on a capacitor could never exceed that of the source. However, large voltages (back emfs) can be generated by inductors when the applied current is suddenly changed.

answered Jan 12, 2017 by sammy gerbil (28,466 points)
selected Jan 13, 2017 by koolman
When switch is off , then at steady state why there will be potential difference between inductor . It is like an zero resistance wire .
An ideal battery also has zero resistance, but it has a potential difference across it. The same is possible for an inductor. Resistors are "passive" circuit elements. They do not store energy, and if the voltage across them changes they do not react to the change. Inductors and capacitors are "reactive" circuit elements. Like a battery they store energy, and they can "react" to changes in the current/voltage by creating a voltage/current to oppose the change.