A charged capacitor is connected to a resistor and a switch as in the figure bel

Question

A charged capacitor is connected to a resistor and a switch as in the figure below. The circuit has a time constant of 1.0 s. After the switch is closed, the charge on the capacitor is 55% of its initial charge.

(a) Find the time it takes to reach this charge.
_____s

(b) If R = 280 k?, what is the value of C?
______ ?F

A charged capacitor is connected to a resistor and a switch as in the figure below. The circuit has a time constant of 1.0 s. After the switch is closed, the charge on the capacitor is 55% of its initial charge. (a) Find the time it takes to reach this charge. _____s (b) If R = 280 k?, what is the value of C? ______ µF

Explanation / Answer

a) Q = Qo e^(-t/CR)
Q=.55Qo so
.55=e^(-t/CR)
ln.55=-t/CR lne
as time constant=1 so RC=1
-.5978=-t
t=.5978 seconds

b)

(b).R = 280 k?

         = 280000 ?

We know ? =RC

From this C = ? /R

                    = 3.571 x 10 -6 F

                    = 3.571 ?F

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