The R C circuit of (Figure 1) has R =7.8k? and C =2.5 ? F . The capacitor is at

Question

The RC circuit of (Figure 1) has R=7.8k? andC=2.5?F . The capacitor is at voltage V0 at t=0,when the switch is closed.

Part A

How long does it take the capacitor to discharge to 0.40{ m %} of its initial voltage?

The RC circuit of (Figure 1) has R=7.8k? andC=2.5?F . The capacitor is at voltage V0 at t=0,when the switch is closed. Part A How long does it take the capacitor to discharge to 0.40{ m %} of its initial voltage? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Here ,

R = 7.8 Kohm

R = 2.5 *10^-6 F

time constant , T = RC

T = 7.8*10^3 * 2.5 *10^-6

T = 0.0195 s

V = Vo*e^(-t/T)

0.40 = e^(-t/.0195)

taking ln

solving for t

t = 0.0179 s

it take 0.0179 s to discharge to 0.40

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