Question

A 7.70-nF capacitor is charged up to 12.0 V , then disconnected from the power supply and connected in series through a coil. The period of oscillation of the circuit is then measured to be 8.10×10−5 s .

Answer 1

Inductance, L = 0.0215 Henry

Step-by-step explanation:

Given that,

Capacitance of the capacitor,
`C=7.7\ nF=7.7* 10^(-9)\ F`

Potential difference, V = 12 V

The period of oscillation,
`t=8.1* 10^(-5)\ s`

At resonance, the angular velocity is given by :

`\omega=(1)/(√(LC) )`

`(2\pi)/(t)=(1)/(√(LC) )`

`L=(t^2)/(4\pi^2C)`

`L=((8.1* 10^(-5))^2)/(4\pi^2* 7.7* 10^(-9))`

L = 0.0215 Henry

So, the inductance of the coil is 0.0215 Henry. Hence, this is the required solution.