In an experiment, $$200\,V\,AC$$   is applied at the ends of an $$LCR$$  circuit. The circuit consists of an inductive reactance
$$\left( {{X_L}} \right) = 50\,\Omega ,$$   capacitive reactance
$$\left( {{X_C}} \right) = 50\,\Omega $$   and ohmic resistance
$$\left( R \right) = 10\,\Omega .$$   The impedance of the circuit is

Solution :
Total effective resistance of $$LCR$$  circuit is called impedance of the $$LCR$$  series circuit. It is represented by $$Z.$$
where $$Z = \frac{{{V_0}}}{{{i_0}}} = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} $$
Given, $${V_{AC}} = 200\,V$$
Resistance offered by inductor $${X_L} = 50\,\Omega $$
Resistance offered by capacitance $${X_C} = 50\,\Omega $$
$$\eqalign{ & R = 10\,\Omega \cr & Z = ? \cr & \therefore Z = \sqrt {{{\left( {10} \right)}^2} + {{\left( {50 - 50} \right)}^2}} \cr & {\text{or}}\,\,Z = 10\,\Omega \cr} $$