Question

For the circuit shown below, find current across \(AB\) \((I_{AB})\). 

• A. \(\frac{10}{7}\ \text{A}\)
• B. \(\frac{13}{7}\ \text{A}\)
• C. \(\frac{11}{7}\ \text{A}\)
• D. \(\frac{15}{7}\ \text{A}\)

Answer 1

The Correct Option is D

Concept: Using superposition and equivalent resistance of parallel branches. Each upper branch contains a \(15\,V\) battery with a \(3\Omega\) resistor. Step 1: Convert branches Current in each source branch: \[ I = \frac{V}{R} = \frac{15}{3} = 5\ \text{A} \] Three such branches supply total current \[ I_{eq} = 5 + 5 + 5 = 15\ \text{A} \] Step 2: Resistance of bottom branch \[ 3\Omega + 3\Omega = 6\Omega \] Step 3: Equivalent resistance Parallel combination of \(1\Omega\) and \(6\Omega\): \[ R_{eq} = \frac{6}{7}\Omega \] Step 4: Current division \[ I_{AB} = \frac{15}{7}\ \text{A} \]