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Q. 81

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 795

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Short Answer

he switch in a closes at and, after a very long time, the capacitor is fully charged. Find expressions for

(a) the total energy supplied by the battery as the capacitor is being charged,

(b) total energy dissipated by the resistor as the capacitor is being charged, and

(c) the energy stored in the capacitor when it is fully charged. Your expressions will be in terms of E, R, and C.

(d) Do your results for parts a to c show that energy is conserved? Explain.

(a) The total energy supplied by the battery as the capacitor is being charged is .

(b) The total energy dissipated by the resistor as the capacitor is being charged is .

(c) The energy stored in the capacitor when it is fully charged is .

(d) The energy of the battery is dissipated into the resistor and the capacitor. Therefore, the energy is conserved through the discharge.

See the step by step solution

Step by Step Solution

Part (a) step 1: Given Information

We need to find the total energy supplied by the battery as the capacitor is being charged.

Part (a) step 2: Simplify

The current in the circuit is given as:

Now, is:

We know that, .

Part (b) step 1: Given Information

We need to find the total energy dissipated by the resistor as the capacitor is being charged.

Part (b) step 2: Simplify

Now we finding the power dissipation :

So, .

Part (c) step 1: Given Information

We need to find the energy stored in the capacitor when it is fully charged. Your expressions will be in terms of and .

Part (c) step 2: Simplify

We finding the energy stored in the capacitor :

Part (d) step 1: Given Information

We need to find that energy is conserved for parts a to c.

Part (d) step 2: Explanation

The energy of the battery is dissipated into the resistor and the capacitor. Therefore, the energy is conserved through the discharge.

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