The R C circuit of (Figure 1) has R =7.7k? and C =4.0 ? F . The capacitor is at

Question

The RC circuit of (Figure 1) has R=7.7k? and C=4.0?F . The capacitor is at voltage V0 at t=0 , when the switch is closed.

How long does it take the capacitor to discharge to 0.25{ m %} of its initial voltage?

Express your answer to two significant figures and include the appropriate units.

The RC circuit of (Figure 1) has R=7.7k? and C=4.0?F . The capacitor is at voltage V0 at t=0 , when the switch is closed. How long does it take the capacitor to discharge to 0.25{ rm %} of its initial voltage? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

time constant = RC= 7.7x103 * 4x10-6=0.0308 s

    Vc( 0) = V0 (initial voltage )

V(infinty) = 0 (final vtg)

The voltage at time t is,

    Vc(t) = V0 * e^(-t/ RC)

    Vc(t) = V0 * e^(-t/ 0.0252)

(0.25/100)* Vo = V0 * e^(-t/ 0.0308)

solving we get, t = 0.1845 s = 0.185 s (rounded)

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