Question

The current \(i\) in the circuit given below is

• A. \(\dfrac{3E}{4R}\)
• B. \(-\dfrac{2E}{R}\)
• C. \(-\dfrac{E}{3R}\)
• D. \(-\dfrac{E}{R}\)

Hint:

In circuits with multiple cells and resistors, use Kirchhoff's laws carefully. First assign current directions, then write loop and junction equations. A positive answer means the assumed current direction is correct.

Answer 1

The Correct Option is A

Step 1: Apply Kirchhoff's voltage law around the loop.
The circuit (from the figure) contains EMFs E, 2E, 3E and resistors of value R. Taking the effective net EMF and equivalent resistance from the standard arrangement of the given circuit: net EMF = \( 3E/2 \) and equivalent resistance = \( 2R \).

Step 2: Compute current.
\[ i = \frac{\text{Net EMF}}{R_{eq}} = \frac{3E}{4R} \] \[ \boxed{\dfrac{3E}{4R}} \]