Question

A short-circuited coil is placed in a time-varying magnetic field. Electrical power ias 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

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

Answer 1

Answer: (B)

The same

Answer 2

Power $P = \frac { e ^ { 2 } } { R }$ ; Here e = induced emf =

$- \frac { d \phi } { d t } = - N A \left( \frac { d B } { d t } \right)$

$R \propto \frac { l } { r ^ { 2 } }$; where R = resistance, r = radius of wire,

l = length of wire ∝ number of turns N (if area of each turn is constant) ⇒ $P \propto \frac { N ^ { 2 } r ^ { 2 } } { l } \propto N r ^ { 2 }$ ⇒ $\frac { P _ { 1 } } { P _ { 2 } } = 1$.