Question:
In the given circuit all resistances are of value \(R\) ohm each. The equivalent resistance between \(A\) and \(B\) is :
In the given circuit all resistances are of value \(R\) ohm each. The equivalent resistance between \(A\) and \(B\) is :
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The two junctions next to A and B, together with the central junction, are joined by plain wires, so they are all at the same potential and the rest of the network carries no current.
Updated On: Nov 11, 2026
- \(2R\)
- \(3R\)
- \(\frac{5R}{3}\)
- \(\frac{5R}{2}\)
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The Correct Option is A
Solution and Explanation
From A, one resistor R leads to the node P. From B, one resistor R leads to the node Q.
P is connected by a plain wire (no resistor) to the central node M; M is connected by a plain vertical wire to the node N below it, and N is connected by a plain wire to Q. Hence P, M, N and Q are all one node (zero resistance between them).
The vertical resistor PQ and the diagonal resistor MQ are shorted by these wires, and every other resistor in the figure (top triangle, right-hand loops, etc.) is connected only to this same single node, so no potential difference appears across them and no current flows through them.
The current path is therefore A - R - (node) - R - B, giving \(R_{eq}=R+R=2R\).
Answer: (1) \(2R\)
P is connected by a plain wire (no resistor) to the central node M; M is connected by a plain vertical wire to the node N below it, and N is connected by a plain wire to Q. Hence P, M, N and Q are all one node (zero resistance between them).
The vertical resistor PQ and the diagonal resistor MQ are shorted by these wires, and every other resistor in the figure (top triangle, right-hand loops, etc.) is connected only to this same single node, so no potential difference appears across them and no current flows through them.
The current path is therefore A - R - (node) - R - B, giving \(R_{eq}=R+R=2R\).
Answer: (1) \(2R\)
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