Question

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

Options

• Halved

• Quadrupled 

• The same

• Doubled

Answer 1

Doubled

Explanation:

P = ${\displaystyle \frac{{\text{e}}^2}{\text{R}}=\frac{{(-\text{NA}\frac{\text{dB}}{\text{dt}})}^2}{\rho \text{l}}\times {\text{A}}_{\text{C}}}$,

A = area of coil

Ac = area of cross section of wire used in coil

P ∝ NA_c

${\displaystyle \frac{{\text{P}}_2}{{\text{P}}_1}=\frac{\frac{\text{N}}{2}\times 4{\text{A}}_{\text{c}}}{{\text{NA}}_{\text{c}}}}$

= 2; P₂ = 2P₁