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 1.40 s. Soon after the switch is closed, the charge on the capacitor is 85.0% of its initial charge.

(a) Find the time interval required for the capacitor to reach this charge.
          s
    
    (b) If R = 200 k?, what is the value of C?
   C =       

A charged capacitor is connected to a resistor and a switch as in the figure below. The circuit has a time constant of 1.40 s. Soon after the switch is closed, the charge on the capacitor is 85.0% of its initial charge.

Explanation / Answer

a)

Q = Qo*e^(-t/T)

0.85*Qo = Qo*e^(-t/1.4)


e^(t/1.4) = 1/0.85

t = 1.4*ln(1/0.85)

= 0.2275 s

b) T = R*C

C = T/R = 1.4/(200*10^3) = 7 micro F

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