Question

Two inductors, \(L_{1}\) and \(L_{2}\), are connected in parallel and time-varying current flows the combination. If \(I_{1}\) and \(I_{2}\) are the currents passing through the inductor \(L_{1}\) and \(L_{2}\) respectively, the ratio \(\frac{I_{2}}{I_{1}}\) is

• A. \(\frac{L_{2}}{L_{1}}\)
• B. \(\frac{L_{1}}{L_{2}}\)
• C. \(\frac{L_{1}}{L_{2}^{2}}\)
• D. \(\frac{L_{2}}{L_{1}^{2}}\)

Hint:

The voltage across parallel inductors is equal, so L1 dI1/dt equals L2 dI2/dt.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Parallel inductors have the same emf at every instant:
\(L_1\dfrac{dI_1}{dt}=L_2\dfrac{dI_2}{dt}\)

Step 2: Integrate
With zero initial currents, \(L_1I_1=L_2I_2\).

Step 3: Ratio
\(\dfrac{I_2}{I_1}=\dfrac{L_1}{L_2}\)

Final Answer:
The current ratio I2 to I1 is L1 over L2. \[ \boxed{\text{(B) }\dfrac{L_{1}}{L_{2}}} \]