Question

The equivalent resistance of the following combination of resistances between \(A\) and \(C\) is:

• A. \(36\,\Omega\)
• B. \(1\,\Omega\)
• C. \(27\,\Omega\)
• D. \(3\,\Omega\)

Hint:

If \(n\) equal resistors of resistance \(R\) are connected in parallel: \[ R_{\text{eq}} = \frac{R}{n} \] Here, \[ 3\Omega \parallel 3\Omega \parallel 3\Omega = \frac{3}{3} = 1\Omega \] Always look for complete paths joining the same two terminals before simplifying a resistor network.

Answer 1

The Correct Option is B

Step 1: Identify the three paths between \(A\) and \(C\). Upper path: \[ A \rightarrow D \rightarrow C \] Resistance: \[ R_1=2+1=3\,\Omega \] Lower path: \[ A \rightarrow B \rightarrow C \] Resistance: \[ R_2=2+1=3\,\Omega \] Diagonal path: \[ A \rightarrow C \] Resistance: \[ R_3=3\,\Omega \]

Step 2: Observe the parallel combination. All three branches connect directly between the same terminals \(A\) and \(C\). Hence the three \(3\,\Omega\) resistors are in parallel. \[ \frac{1}{R_{\text{eq}}} = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} \] \[ \frac{1}{R_{\text{eq}}} = 1 \] Therefore, \[ R_{\text{eq}} = 1\,\Omega \]

Step 3: Select the correct option. \[ \boxed{R_{\text{eq}}=1\,\Omega} \] Hence, the correct answer is: \[ \boxed{\text{(B)}} \]