A resistance $$'R'$$ draws power $$'P'$$ when connected to an $$AC$$  source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes $$'Z'$$ the power drawn will be

Solution :
When a resistor is connected to an $$AC$$ source. The power drawn will be
$$P = {V_{rms}} \cdot {I_{rms}} = {V_{rms}} \cdot \frac{{{V_{rms}}}}{R} \Rightarrow V_{rms}^2 = PR$$
When an inductor is connected in series with the resistor, then the power drawn will be
$$P' = {V_{rms}} \cdot {I_{rms}}\cos \phi $$
where, $$\phi = $$ phase difference
$$\eqalign{ & \therefore P' = \frac{{V_{rms}^2}}{R} \cdot \frac{{{R^2}}}{{{Z^2}}} = P \cdot R \cdot \frac{R}{{{Z^2}}} \cr & \Rightarrow P' = \frac{{P \cdot {R^2}}}{{{Z^2}}} = P{\left( {\frac{R}{Z}} \right)^2} \cr} $$