Question

A series LCR circuit is connected to a 220 V ac source of variable frequency. The inductance of the coil is 5H, capacitance of the capacitor is 5$\mu$ F and resistance is 40 $\Omega$. Its resonance, calculate
1) The resonant frequency
2)Current in the circuit
3)The inductive reactance

Answer 1

$1.$ Resonance frequency $f=\frac{1}{2\pi \sqrt{LC}}$

$f=\frac{1}{2\pi \sqrt{5\times 5\times {10}^{-6}}}=\frac{1000}{10\pi }=\frac{100}{10\pi }=31.8$ $H_z$

$\omega =200$ $rad/s$

$2.$ Current at resonance. $I_r=\frac{220}{R}=\frac{220}{40}=5.5$ $A$

$3.$ $X_L=\omega L=200\times 5=1000$ $\Omega$