Question

In an LC circuit in which C = 4.0 uF the maximum potential difference across the capacitor during the oscillations is 1.5 V and the maximum current through the inductor is 50 mA. (a) What is the inductance L? (b) What is the frequency of the oscillations? (c) How much time does it take for the charge on the capacitor to rise from zero to its maximum value?

Answer 1

$C=4.0\mu F$

V=1.5Volt

I=50mA

We know that

$I=\frac{V}{X_c}$

$I=V wc$

$I=2\pi fcV$

$f=\frac{I}{2\pi cV}$

Put value

$f=\frac{50\times10^{-3}}{2\pi\times4\times10^{-6}\times1.5}=1326.96Hz$

Part(a)

Inductance

$L=\frac{V}{2\pi f I}$

$$L=\frac{1.5}{2\pi \times1326.96\times50\times10^{-3}}=3.6\times10^{-3}F$$

Part(b)

$f=\frac{I}{2\pi cV}$

$f=\frac{50\times10^{-3}}{2\pi\times4\times10^{-6}\times1.5}=1326.96Hz$

Part(c)

We know that

$V=IR$

$R=\frac{V}{I}$

$R=\frac{1.5}{50\times10^{-3}}=30\Omega$

Time (T)=RC

Capacitor are maximum charge

$T=30\times4\times10^{-6}=0.12msec$