Question

A short circuited coil is placed in a time varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be –

• A. Halved
• B. The same
• C. Doubled
• D. Quadrupled

Answer 1

Answer: (B)

The same

Answer 2

As power dissipated P =$\frac{e^{2}}{R}$Here, e = induced e.m.f. = –$\left( \frac{d\varphi}{dt} \right)$and f = NBA \ e = – NA$\left( \frac{dB}{dt} \right)$

Also, we know that R µ$\frac{\mathcal{l}}{a}$µ$\frac{\mathcal{l}}{r^{2}}$

\ P =$\frac{e^{2}}{R}$µ$\frac{N^{2}A^{2}r^{2}}{\mathcal{l}}$µ$\frac{N^{2}r^{4}}{\mathcal{l}}$

According to the question

r, radius is halved and N, number of turns is quadrupled.

\ P remains the same.