Question

Three identical capacitors are connected with a resistor in two different circuits. When they are connected in series, the time constant to charge up this circuit is 0.02s. What is the time constant when they are connected as in parallel?

Answer 1

Explanations & Calculations

• The time constant is $\small \tau=RC$
• When the cap.s are in series

$\qquad\qquad \begin{aligned} \small C_{equivalent}&=\small \frac{C}{3}\\ \therefore\quad\small 0.02\,s&=\small R\frac{C}{3}\\ \small RC&=\small 0.06\,s \end{aligned}$

• When they are in parallel connection

$\qquad\qquad \begin{aligned} \small C_{equivalent}&=\small 3C\\ \small \tau&=\small R(3C)\\ &=\small 3\times0.06\,s\\ &=\small 0.18\,s \end{aligned}$