Four resistors of \( 6\,\Omega \) resistance each are joined as shown in the figure. The equivalent resistance of the combination is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 8\,\Omega \)
A connecting wire has no resistance, so the two points it joins are at the same potential and can be treated as one node.
Name the resistors 1, 2, 3, 4 from A to B. The upper wire joins the left end of resistor 1 to the junction between resistors 2 and 3; call this node X. The lower wire joins the junction between resistors 1 and 2 to the junction between resistors 3 and 4; call this node Y.
\( \text{Resistor 1: X to Y} \)
\( \text{Resistor 2: Y to X} \)
\( \text{Resistor 3: X to Y} \)
So resistors 1, 2 and 3 are all in parallel between X and Y, and resistor 4 is in series with them, from Y to B.
\( \displaystyle R_{XY} = \frac{6}{3} = 2\,\Omega \)
\( \displaystyle R_{AB} = 2\,\Omega + 6\,\Omega = 8\,\Omega \)