   Chapter 18, Problem 38P

Chapter
Section
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 ε is 9.00V, Resistance R is 55.0Ω, Time constant τ and t is 0

The maximum charge on the capacitor

Qmax=Cε(1e(tτ))

The Potential difference across the capacitor

Vcap=QmaxC

Use cε[1et/τ] for Qmax in the above equation to find expression for Vc

Vc=Cε(1e(tτ))C=ε(1e(tτ))

Apply Kirchhoff’s loop rule

εIRVcap=0

Use ε[1et/τ] 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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