Question

An inductance of 2.0 H, a capacitance of $18\mu F$ and a resistance of 10$k\Omega$ are connected to an AC source of 20 V with adjustable frequency. (a) What frequency should be chosen to maximise the current in the circuit? (b) What is the value of this maximum current ?

Answer 1

(a) For current to be maximum in a circuit
$X_L=X_C$ (Resonant Condition)

$\Rightarrow \omega L=\frac{1}{\omega C}$

$\Rightarrow {\omega }^2=\frac{1}{LC}=\frac{1}{2\times 18\times {10}^{-6}}$

=$\frac{{10}^6}{36}$

$\Rightarrow \omega =\frac{{10}^3}{6}\Rightarrow 2\pi f=\frac{{10}^3}{6}$

$\Rightarrow f=\frac{1000}{6\times 2\pi }$ = 26.539 Hz

= 27 Hz.

(b) Maximum current

= $\frac{E}{R}=\frac{20}{10\times {10}^3}$

= $\frac{2A}{{10}^3}$ = 2mA

(Inresonance condition)