A transformer is used to light a $$100\,W$$  and $$110\,V$$  lamp from a $$220\,V$$  mains. If the main current is $$0.5\,A,$$  the efficiency of the transformer is approximately

Solution :
The efficiency of transformer $$ = \frac{{{\text{Energy obtained from the secondary coil}}}}{{{\text{Energy given to the primary coil}}}}$$
$${\text{or}}\,\,\eta = \frac{{{\text{Output power}}}}{{{\text{Input power}}}}$$
$$\eqalign{ & {\text{or}}\,\,\eta = \frac{{{V_s}{I_s}}}{{{V_p}{I_p}}}\,\,\left[ {{\text{as}}\,{\text{power}} = VI} \right] \cr & {\text{Given,}}\,\,{V_s}{I_s} = 100\,W,\,{V_p} = 220\,V,\,{I_p} = 0.5\,A \cr & {\text{Hence,}}\,\eta = \frac{{100}}{{220 \times 0.5}} = 0.90 = 90\% \cr} $$