Question

Two inductors, \(L_{1}\) and \(L_{2}\) are connected in parallel and a time varying current flows as shown in the figure. The ratio of currents \(\frac{I_{2}}{I_{1}}\) at any time, it is

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

Hint:

Parallel inductors have the same voltage, so \(L_{1}\frac{dI_{1}}{dt}=L_{2}\frac{dI_{2}}{dt}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The potential difference across both inductors in parallel is the same: \(L_{1}\frac{dI_{1}}{dt}=L_{2}\frac{dI_{2}}{dt}\).

Step 2: Integrate
Assuming the currents start from zero, \(L_{1}I_{1}=L_{2}I_{2}\).

Step 3: Ratio
\(\frac{I_{2}}{I_{1}}=\frac{L_{1}}{L_{2}}\).

Step 4: Compare the options
This is option (B).

Final Answer:
The ratio \(\frac{I_{2}}{I_{1}}\) equals \(\frac{L_{1}}{L_{2}}\). \[ \boxed{\text{(B) }\dfrac{L_{1}}{L_{2}}} \]