Q.15. An inductor L, a capacitor C and a resistor R are connected in series in an a.c. circuit. Deduce, with the help of suitable phasor diagrams, a mathematical expression for impedance of this circuit. What  is meant by resonance of this circuit? Prove that this circuit exhibits resonance at a frequency given by $\frac{1}{2\mathrm{\pi }\sqrt{\mathrm{LC}}}$.