A $100mH$ inductor, a $25\mu F$ capacitor and a $15\Omega$ resistor are connected in series to a $120V$, $50Hz$ ac source. Calculate
(a) impedance of the circuit at resonance
(b) current at resonance
(c) resonant frequency

(i) At resonance, the $L C R$ circuit is purely resistive. $Z_{\text {min }}=R=15 \Omega$

(ii) Current at resonance

$=\frac{120 \mathrm{~V}}{15 \Omega}=8 \mathrm{~A}$

(iii) Resonant frequency, $f$

$\begin{array}{l} =\frac{1}{2 \pi \sqrt{L C}} \\ = \frac{7}{2 \times 22 \times \sqrt{100 \times 10^{-3} \times 25 \times 10^{-6}}} \mathrm{~Hz} \\ = \frac{3182}{0.316} \mathrm{~Hz}=100.7 \mathrm{~Hz} \end{array}$