Question

If power dissipated in a coil having total number of turns 'N', cross-section area 'A' and radius of coil 'R' when kept in a time varying magnetic field is P. Now if another coil having total number of turns '2N', cross-section area '2A' and radius of coil '3R' is placed is same time varying magnetic field power dissipated is $\alpha P$, then value of $\alpha$ is :

• A. 108
• B. 324
• C. 216
• D. 432

Answer 1

The Correct Option is A

Step 1: Express power in terms of coil parameters.
$P = \frac{V^2}{R_c}$ where $V = N \pi R^2 \frac{dB}{dt}$ and $R_c = \rho \frac{2\pi R N}{A}$.
$P \propto \frac{(N R^2)^2}{RN/A} = \frac{N^2 R^4 A}{RN} = N R^3 A$.

Step 2: Compare the two cases.
$P_1 \propto N R^3 A$.
$P_2 \propto (2N) (3R)^3 (2A) = 2N \cdot 27R^3 \cdot 2A = 108 (N R^3 A)$.

Step 3: Find $\alpha$.
$P_2 = 108 P_1 \implies \alpha = 108$.

Final Answer: Option (1).