Find the following: A 20 mu F capacitor is connected in series with a 160 Ohm re

Question

Find the following:

A 20 mu F capacitor is connected in series with a 160 Ohm resistor. The capacitor is initially charged to a voltage of 50V. Find how long it takes for the voltage to drop to 10V. A 20 mu F capacitor is connected in series with an unknown resistor. The capacitor is initially charged to 50V. The voltage drops to 10V after 8.0 ms. Find the unknown resistance. A 12.0V ideal battery is used to charge up a 5.0 mu F capacitor via a 1.2M Ohm resistor. Find how long it takes for the voltage on the capacitor to reach 8.0V.

Explanation / Answer

equation for volatge in RC ckt while discharging is V= V0(e^-t/RC)
so e^-t/RC = 10/50 = 0.2

-t/RC = ln (0.2) = -1.609
t = 1.609 *RC   

t = 1.609 * 160 * 20*10^-6

t = 5.15 ms

b. againg e^-t/RC = 10/50 = 0.2

-t/RC = ln (0.2) = -1.609

RC = 0.008/1.609 =0.00497

R = 0.00497/20uF = 248.6 ohms

c. apply e^-t/RC = 8/12 = 0.6667

-t/Rc = ln(0.66667) = -0.405

t = 0.405 * 5uF*1.2*10^6

t = 2.43 secs

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