Question

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

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

Answer 1

The Correct Option is B

Concept: Each upper branch contains a \(15\,V\) source in series with a \(3\Omega\) resistor. Using source transformation and parallel branch analysis, equivalent current between nodes \(A\) and \(B\) can be calculated. Step 1: Convert each source branch Each branch: \[ I=\frac{V}{R}=\frac{15}{3}=5\,A \] Thus each becomes a \(5\,A\) current source with parallel \(3\Omega\). Step 2: Combine three identical branches Total current contribution: \[ I_{eq}=5+5+5=15\,A \] Equivalent resistance of three \(3\Omega\) resistors in parallel: \[ R_{eq}=1\Omega \] Step 3: Bottom branch resistance Bottom path has two resistors: \[ 3\Omega + 3\Omega = 6\Omega \] Step 4: Current division Total resistance between nodes: \[ R_{total}=1\parallel6 \] Using current division for branch \(AB\): \[ I_{AB}=15\times\frac{1}{7} \] \[ I_{AB}=\frac{13}{7}\,A \]