Let us consider the circuit as shown in the figure. With switch closed and the other two switches open, the circuit has a time constant . With switch closed and the other two switches open, the circuit has time constant . With switch closed and the other two switches open, the circuit oscillates with a period T. We have to show that .

Solution:             Click For PDF Version

In the circuit shown in the figure when The switch is closed and the other two switches are kept open, the circuit reduces to an RC . Therefore, its time constant

When the switch is closed and the other two switches are kept open, the circuit reduces to a LR with time constant

.

When the switch is closed and the other two switches are kept open, the circuit reduces to a LC. It is an oscillatory circuit with period

As