Question

In the given circuit, if \(dI/dt = -1 \text{A/s}\) then the value of \(V_{AB}\) at this instant will be

• A. \(30\text{V}\)
• B. \(20\text{V}\)
• C. \(10\text{V}\)
• D. \(15\text{V}\)

Hint:

Add the drops and rises along the path from A to B, including the induced emf of the inductor.

Answer 1

The Correct Option is D

Step 1: Add the sources
The resistor drop is $12$ V from A. The inductor drops $L\,dI/dt = -3$ V (a rise of 3 V because the current decreases). The cell drops $6$ V.

Step 2: Net
Total drop from A to B $= 12 - 3 + 6 = 15$ V. Option (D).

Final Answer:
15 V. \[ \boxed{\text{(D)}\ 15\ \text{V}} \]