Thank you for reporting, we will resolve it shortly
Q.
What is the value of inductance L for which the current in a maximum in a series L-C-R circuit with C = 10 $\mu$F and $\omega = 1000 s^{ - 1}$ ?
Alternating Current
Solution:
Current in L-C-R series circuit,
$ i = \frac{ V}{ \sqrt{ R^2 + ( X_L - X_C)^2 }} $
For current to be maximum, denominator should be minimum which can be done, if
$ X_L - X_C $
This happens in resonance state of the circuit i, e,
$ \omega L = \frac{ 1}{ \omega C } $
or L = $ \frac{ 1}{ \omega^2 C } $ $$ ..(i)
Given, $ \omega = 1000\, s^{ - 1}, \, C = 10 \, \mu F = 10 \times 10^{ - 6} \, F$
Hence, $ L = \frac{ 1}{ (1000)^2 \times 10 \times 10^{ - 6}} $
= 0.1 H
= 100 m H.