Question

The effective resistance between \(A\) and \(B\) is _ _ _, where \(R=3\,\Omega\).

• A. \(\dfrac{5}{3}\,\Omega\)
• B. \(5\,\Omega\)
• C. \(3\,\Omega\)
• D. \(\dfrac{3}{5}\,\Omega\) \bigskip

Hint:

Before solving a resistor network, first merge all points connected by ideal wires into single nodes. Then identify series and parallel combinations between those nodes.

Answer 1

The Correct Option is B

Concept: Identify nodes connected by ideal wires; resistors between same nodes are in parallel. Compute equivalent resistance.

Step 1: Upper branch: \(R+2R+3R=6R\). Middle: \(R+2R=3R\). Lower: \(2R+3R+5R=10R\). All between A and B in parallel.

Step 2: \(1/R_{eq} = 1/(6R) + 1/(3R) + 1/(10R) = 3/(5R) \Rightarrow R_{eq} = 5R/3\). With \(R=3\,\Omega\), \(R_{eq}=5\,\Omega\).

Step 3: Write the final answer. \(\boxed{R_{\text{eq}}=5\,\Omega}\)