A coil has resistance 30 ohm and inductive reactance 20 ohm at $$50\,Hz$$  frequency. If an $$ac$$  source, of 200 volt, $$100\,Hz,$$  is connected across the coil, the current in the coil will be

Solution :
$$\eqalign{ & {\text{If}}\,\omega = 50 \times 2\pi \,{\text{then}}\,\omega L = 20\Omega \cr & {\text{If}}\,\omega ' = 100 \times 2\pi \,{\text{then}}\,\omega 'L = 40\Omega \cr} $$
Current flowing in the coil is
$$\eqalign{ & I = \frac{{200}}{Z} = \frac{{200}}{{\sqrt {{R^2} + {{\left( {\omega 'L} \right)}^2}} }} = \frac{{200}}{{\sqrt {{{\left( {30} \right)}^2} + {{\left( {40} \right)}^2}} }} \cr & I = 4A. \cr} $$