# Finding the maximum value of current through the inductor

• Rick001
In summary, the conversation discusses a problem involving a circuit with a switch and two capacitors. The first two parts are solved, but there is trouble with the third part. The individual explains their attempt at finding the solution, but it does not match the given answer. The expert points out an error in the assumption made about the energy in the inductor and confirms that the rest of the work is correct.
Rick001

## The Attempt at a Solution

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I got the first 2 parts, but I'm having trouble with the last one. For the time the switch S1 is closed, I derived ##q(t) = CE(1 - \cos(\frac{t}{\sqrt{LC}}))##, by writing the loop equation ##\frac{E}{L} - \frac{1}{LC}q = \frac{d^2 q}{dt^2}##, from that we get charge on the capacitor after t0 to be CE and differentiating my expression, we get current at t=t0 to be ##\frac{CE}{\sqrt{LC}}##, after closing S2 and opening S1, we have a loop where the inductor has a current ##\frac{CE}{\sqrt{LC}}## flowing through it and one capacitor has a charge CE, the other is uncharged. Now for the third part of the question, I tried finding the total energy of the components currently connected, we get a total of CE², I thought equating this to ½L(Imax)² would give me the answer, but none of them match. Why does this not work? Where is my working wrong? The answer for the last part is given as (c)

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Welcome to PF!

Rick001 said:
we get a total of CE², I thought equating this to ½L(Imax)² would give me the answer, but none of them match.
You are assuming that when the current is at its maximum, all of the energy is in the inductor.

All of your other work looks correct to me.

## 1. How do you find the maximum value of current through an inductor?

The maximum value of current through an inductor can be found by using the formula I(max) = V/R, where V is the voltage across the inductor and R is the resistance in the circuit.

## 2. What factors affect the maximum value of current through an inductor?

The maximum value of current through an inductor is affected by the voltage across the inductor, the resistance in the circuit, and the inductance of the inductor itself.

## 3. Can you exceed the maximum value of current through an inductor?

It is possible to exceed the maximum value of current through an inductor, but this can damage the inductor and other components in the circuit. It is important to carefully calculate and limit the current to avoid exceeding the maximum value.

## 4. How does the inductance of an inductor affect the maximum current value?

The inductance of an inductor is directly proportional to the maximum current value. This means that as the inductance increases, the maximum current value also increases.

## 5. Can the maximum value of current through an inductor change over time?

The maximum value of current through an inductor can change over time if the voltage or resistance in the circuit changes. However, the inductance of the inductor remains constant, so the maximum current value will not change unless there is a change in the circuit parameters.

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