In a given network, each resistance has value of \(6 \Omega\). The point \(\mathrm{X}\) is connected to point \(\mathrm{A}\) by a copper wire of negligible resistance and point \(Y\) is connected to point B by the same wire. The effective resistance between \(\mathrm{X}\) and \(\mathrm{Y}\) will be

• A

  \(18 \Omega\)
• B

  \(6 \Omega\)
• C

  \(3 \Omega\)
• Correct answer
  D

  \(2 \Omega\)

Solution

One end of all the three resistors are connected at the point \(X\) and the other at the point \(Y\). Therefore, the equivalent circuit is given below:
The equivalent resistance is given by \(\begin{aligned} & \frac{1}{R}=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{3}{6}=\frac{1}{2} \\ & \Rightarrow R_{\text {eq }}=2 \Omega \end{aligned}\)

Hence, the correct answer is option: 'D'.