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.
(c) $l$ increases and $A$ decreases.
(d) both $l$ and $A$ decrease.
[NCERT Exemplar]
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Solution:
Ans. Correct option : (b)
Explanation : As we know that,
$$ L=\mu_{r} \mu_{0} \frac{N^{2} A}{l} $$
As $L$ is constant for a coil,
$$ L \propto A \text { and } L \propto \frac{1}{l} $$
As $\mu_{r}$ 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.
