Find the equivalent resistance between two ends of the following circuit

Solution

Physics sir · 3 steps

Follow the two bare wires and label the nodes: all three resistors join the same two points.

1. Label the nodes. Call the left terminal A and the right terminal B. The top wire joins A to the point between the second and third resistors, so that point is also A. The bottom wire joins B to the point between the first and second resistors, so that point is also B.
2. Check each resistor. The first r/3 runs from A to B. The second runs from B to A. The third runs from A to B. Every resistor sits between the same two nodes, so all three are in parallel.

   1/R_(eq) = 3/r + 3/r + 3/r = 9/r

3. So. R_(eq) = r/9, which is option (d).

The idea to keep. A plain wire has no resistance, so both of its ends are the same node. Give every junction a node name first, then see which two nodes each resistor connects.

Answer from the NTA final answer key. Solution by PrepWiser.