Consider the circuit shown in figure . With switch `S_(1)` closed and the other two switches open, the circuit has a time constant `0.05 sec`. With switch `S_(2)` closed and the other two switches open, the circuit has a time constant 2 sec. With switch `S_(3)` closed and the other two switches open, the circuit oscillates with a period T. Find T ( in sec ) . ( Take `pi ^(2)=10)`

Answer

2

Explanation

`tau_(1)=RC,tau_(2)=(L)/(R)impliesLC=tau_(1)tau_(2)=0.1sec`
`impliesT=2pi sqrt(LC)=2pisqrt((1)/(10))=2sec`