Chapter 18, Problem 38P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# The capacitor in Figure P18.35 is uncharged for t < 0. If ε = 9.00 V, R = 55.0 Ω , and C = 2.00 μF, use Kirchhoff’s loop rule to find the current through the resistor at the times: (a) t = 0, when the switch is closed, and (b) t = τ, one time constant after the switch is closed.

(a)

To determine

The current I through the resistor at the times t=0 when the switch is closed.

Explanation

Given Info: Electromotive force Îµ is 9.00â€‰V, Resistance R is 55.0â€‰Î©, Time constant Ï„ and t is 0

The maximum charge on the capacitor

â€‚Â Qmax=CÎµ(1âˆ’e(âˆ’tÏ„))

The Potential difference across the capacitor

â€‚Â Vcap=QmaxC

Use cÎµ[1âˆ’eâˆ’t/Ï„] for Qmax in the above equation to find expression for Vc

â€‚Â Vc=CÎµ(1âˆ’e(âˆ’tÏ„))C=Îµ(1âˆ’e(âˆ’tÏ„))

Apply Kirchhoffâ€™s loop rule

â€‚Â Îµâˆ’IRâˆ’Vcap=0

Use Îµ[1âˆ’eâˆ’t/Ï„] for V

(b)

To determine

The current I through the resistor at the times t=τ when the switch is closed.

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