Match the following scenarios involving inductors with their corresponding energy or inductance values. List - I List - II (P) Energy stored in an inductor of inductance L carrying current I (1) L 1

Question

Match the following scenarios involving inductors with their corresponding energy or inductance values.

List - I	List - II
(P) Energy stored in an inductor of inductance L carrying current I	(1) $L_{1} + L_{2} + 2 M$
(Q) Equivalent inductance of two inductors $L_{1}, L_{2}$ in series, aiding	(2) $\frac{1}{2} L I^{2}$
(R) Equivalent inductance of two inductors $L_{1}, L_{2}$ in series, opposing	(3) $μ_{0} \frac{N ^{2}}{l} A$
(S) Self-inductance of a long solenoid with N turns, length l, area A	(4) $L_{1} + L_{2} - 2 M$

TestHub · Accepted Answer

The energy stored in an inductor is U = 2 1 ​ L I 2 (P-2). For two inductors L 1 ​ , L 2 ​ in series with mutual inductance M , the equivalent inductance is L e q ​ = L 1 ​ + L 2 ​ + 2 M when aiding (Q-1) and L e q ​ = L 1 ​ + L 2 ​ − 2 M when opposing (R-4). The self-inductance of a long solenoid is L = μ 0 ​ n 2 A l = μ 0 ​ ( N / l ) 2 A l = μ 0 ​ l N 2 ​ A (S-3).

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