Q. 81

Expert-verifiedFound in: Page 795

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

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.

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

The current in the circuit is given as:

Now, is:

We know that, .

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

Now we finding the power dissipation :

So, .

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

We finding the energy stored in the capacitor :

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

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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