SATHEE: electromagnetic-induction Question 20

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Question: Q. 1. The self-inductance $L$ of a solenoid of length $l$ and area of cross-section $A$ , with fixed number of turns $N$ increases as

(a) $l$ and $A$ increase.

(b) $l$ decreases and $A$ increases.

(d) both $l$ and $A$ decrease.

[NCERT Exemplar]

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Solution:

Ans. Correct option : (b)

Explanation : As we know that,

$L = μ_{r} μ_{0} \frac{N^{2} A}{l}$

As $L$ is constant for a coil,

$L \propto A and L \propto \frac{1}{l}$

As $μ_{r}$ and $N$ are constant here so, to increase $L$ for a coil, area $A$ must be increased and $l$ must be decreased.

Important point : The self and mutual inductance of capacitance and resistance depend on the geometry of the devices as well as permittivity/permeability of the medium.

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