# An RC series circuit contains a resistor having resistance R = 2.1 kΩ and acapacitor with capacitance C = 18 μF. Assuming that the capacitor beginsfully charged, but with the wrong polarity,...

An RC series circuit contains a resistor having resistance R = 2.1 kΩ and a

capacitor with capacitance C = 18 μF. Assuming that the capacitor begins

fully charged, but with the wrong polarity, determine the time it takes for

the capacitor be become uncharged.

(a) 20.2 msec (b) 26.2 msec (c) 32.2 msec

(d) 38.2 msec (e) 44.2 msec (f) None of the above.

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### 1 Answer

The RC series circuit contains a resistor having resistance R = 2.1 kΩ and a

capacitor with capacitance C = 18 μF. The capacitor is initially fully charged, but with the wrong polarity. It discharges through the resistor.

The equation relating the voltage across the capacitor, when it is charging, at time t if the resistance is R and the capacitance is C is` V(t) = V_0*(1 - e^(-t/(RC)))` and the equation when the capacitor is discharging is `V(t) = V_0*e^(-t/(RC))`

Here, R = 2.1 kΩ and C = 18 μF. Solving `V_0*(1 - e^(-t/(RC))) = V_0*e^(-t/(RC))` gives `e^(-t/(RC)) = 1/2`

`ln(0.5) = -t/(18*2.1*10^-3)`

`t ~~ 26.2` ms

The time is takes for the capacitor to get discharged is equal to 26.2 ms

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