Question

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

Answer 1

For current to be maximum in a circuit

$X_l=X_C$(Resonant Condition)

$W_l=\frac{1}{W_c}$

$W^2=\frac{1}{L_c}=\frac{1}{2\ast 18\ast {10}^{-6}}=\frac{{10}^6}{36}$

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

$f=\frac{1000}{6\ast 2\pi }=27Hz$

$Max.current=\frac{20}{10\ast {10}^3}=2mA.$