If both the number of turns and length of an inductor are tripled, keeping other factors constant, the self-inductance of the inductor will be |
tripled doubled four times its initial value Unchanged |
tripled |
The correct answer is Option (1) → tripled Self-inductance of a solenoid: $L = \mu_0 \frac{N^2 A}{l}$, where N = number of turns, l = length of solenoid, A = cross-sectional area Let original inductance be $L_0 = \mu_0 \frac{N^2 A}{l}$ If number of turns is tripled: $N' = 3N$ If length is tripled: $l' = 3l$ New inductance: $L' = \mu_0 \frac{(3N)^2 A}{3l} = \mu_0 \frac{9 N^2 A}{3 l} = 3 \mu_0 \frac{N^2 A}{l} = 3 L_0$ ∴ Self-inductance becomes three times the original value |