Question

A current of \(3\,\text{A}\) flows through the following circuit in anticlockwise direction as well as in clockwise direction. The value of \(E\) respectively is

• A. \(3\,\text{V},\ 7\,\text{V}\)
• B. \(4\,\text{V},\ 8\,\text{V}\)
• C. \(6\,\text{V},\ 10\,\text{V}\)
• D. \(1\,\text{V},\ 19\,\text{V}\)

Hint:

Always assume a current direction first; a negative emf indicates opposite polarity.

Answer 1

The Correct Option is D

Step 1: Identify total resistance.
The resistances \(2\,\Omega\) and \(1\,\Omega\) are in series.
\[ R_{\text{total}} = 2 + 1 = 3\,\Omega \]
Step 2: Case I — Current in anticlockwise direction.
Applying Kirchhoff’s loop law:
\[ E + 10 = I R \] \[ E + 10 = 3 \times 3 = 9 \] \[ E = 9 - 10 = -1\,\text{V} \] Magnitude of \(E = 1\,\text{V}\).

Step 3: Case II — Current in clockwise direction.
Now the sources oppose each other:
\[ 10 - E = I R \] \[ 10 - E = 9 \] \[ E = 19\,\text{V} \]
Step 4: Conclusion.
The value of \(E\) is \(1\,\text{V}\) for anticlockwise current and \(19\,\text{V}\) for clockwise current.