1. A RC circuit has a 22 mF (22 x 10^-3 F) capacitor and a 330 ohm resistor. (a)

Question

1. A RC circuit has a 22 mF (22 x 10^-3 F) capacitor and a 330 ohm resistor.

(a) What is the time constant?

(b) If the capacitor is initially charged to 13.5 V, what is the voltage after 20 seconds?

2. A real capacitor can be modeled as a capacitor in parallel with a resistor. The resistor in parallel accounts for the slow leakage of charge from the capacitor. If such a real capacitor has a capacitance of 47 microF (or 47 x 10^-6 F), and is charged to 20 V at time t = 0, if it has a voltage of 4.714 V across it 1800 s later (30 min), what would the modeled value of the internal resistance be? Hint: if you know the time and want the voltage, you use V (t) = Vo e^(-t/Tau) , so if you have the voltage and want the time, consider dividing both sides by Vo and then taking the natural log of both sides.

Explanation / Answer

1. a. tau = RC = 22.0E-3*330= 7.26 s

b) V capacitor = V0 e^(-t/tau) = 13.5*e^(-7.26/20)= 9.39 V

2. V = V0 e^(-t/tau)

4.714 =20e^(-1800/tau)

4.714 /20= e^(-1800/tau)

ln(4.714/20) = -1800/tau

tau = RC

ln(4.714/20) = -1800/(R*47.0E-6)

R=2.65E7

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