Question

A 100 uF capacitor is placed in a series with a 330 uF capacitor. This combination is then placed in a series with a 220 k-ohm resistor and an emf V. What is the time constant of this circuit?

A. 7.67 s

B. 7.67 s^-1

C. 43.0 s^-1

D. 16.9  

Answer 1

The RC time constant, also called tau, the time constant (in seconds) of an RC circuit, is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e.

time constant = R*C

R = 220 kΩ = 2.2 * 10^5 Ω

now first we have to find the equivalent capacitance of the circuit,

so, two capacitors of 100 μF and 330 μF are connected in series so their equivalent capacitance is,

1/C = 1/C1 + 1/C2

C = (C1*C2) /(C1+ C2)

C = (100 * 10^-6 * 330 * 10^-6) / ( 100 * 10^-6 + 330 * 10^-6)

C = 7.674 * 10^-5 F

now putting R and C to get time constant,

time constant = (2.2 * 10^5) * ( 7.67 * 10^-5)

time constant = 16.87 ~ 16.9

so, D is the correct answer.