First slide

Inductance

Question

Two inductors L₁ and L₂ are connected in parallel and a time varying current flows as shown.
The ratio of currents i₁/i₂ at any time / is

Moderate

A

$L_{1} / L_{2}$
B

$L_{2} / L_{1}$
C

$\frac{L_{1}^{2}}{{(L_{1} + L_{2})}^{2}}$
D

$\frac{L_{2}^{2}}{{(L_{1} + L_{2})}^{2}}$

Solution

The inductors are in parallel. Therefore, potential difference across them is same.
Hence , V₁ = V₂
$or L_{1} (\frac{{di}_{1}}{dt}) = L_{2} (\frac{{di}_{2}}{dt})$
$or L_{1} ({di}_{1}) = L_{2} ({di}_{2})$
Integrating, we get
$L_{1} i_{1} = L_{2} i_{2}$
$or \frac{i_{1}}{i_{2}} = \frac{L_{2}}{L_{1}}$

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