Question

i) a transformer is used to light 140 watt 24 volt lamp from 240 volt AC mains. the current in the main cable is 0.7 A. the efficiency of the transformer is?
ii) an inductor coil stores 32J of magnetic field energy & dissipates energy as heat at the rate of 320 W, when a current of 4 A is passed through it. the time constant of the circuit when this coil is joined across an ideal battery will be?

Answer 1

Dear Student,

$$\begin{gathered} \left(1\right)\mathrm{Output}\mathrm{Power}=140\mathrm{W} \\ \mathrm{input}\mathrm{power}=240\times 0.7=168\mathrm{W} \\ \mathrm{Efficiency}=\frac{\mathrm{Output}\mathrm{power}}{\mathrm{input}\mathrm{power}}\times 100\% \\ \mathrm{Efficiency}=\frac{140}{168}\times 100\%=83.33\% \\ \left(2\right)\mathrm{Energy}\mathrm{stored},\mathrm{E}=\frac{1}{2}{\mathrm{Li}}^2 \\ 32=\frac{1}{2}\mathrm{L}\times {\left(4\right)}^2 \\ \mathrm{L}=\frac{64}{16}=4\mathrm{H} \\ \mathrm{P}={\mathrm{i}}^2\mathrm{R} \\ 320={\left(4\right)}^2\mathrm{R} \\ \mathrm{R}=\frac{320}{16}=20\mathrm{ohm} \\ \mathrm{Time}\mathrm{constant},\mathrm{t}=\frac{\mathrm{L}}{\mathrm{R}} \\ \mathrm{t}=\frac{4}{20}=0.2\mathrm{s} \end{gathered}$$