A coil is placed in a time varying magnetic field. If the number of...

(\mathrm{P}=\frac{\varepsilon^2}{R}) where, (\varepsilon=) inducedemf (=-\frac{d \phi}{d t}) (\phi=\mathrm{NBA}) (\varepsilon=\mathrm{NA} \frac{\mathrm{dB}}{\mathrm{dt}}) also, (R \propto \frac{1}{\mathrm{r}^2}) where, (\mathrm{R}=) resistance and (\mathrm{r}=) radius of wire ($$\begin{aligned} & \mathrm{P} \propto \frac{\mathrm{N}^2 \mathrm{r}^2}{\mathrm{H}^2} \\ & \frac{\mathrm{P}_1}{\mathrm{P}_2}=1 \\ & \mathrm{P}_1=\mathrm{P}_2 \end{aligned}$$) This means if the number of turns were quadrupled and the wire radius halved, the electrical power dissipated would be remains same.