Three $2 \Omega$ resistors are connected to form a triangle. The resistance between any two corners is

• Correct answer
  A

  $\frac{4}{3} \Omega$
• B

  $\frac{3}{4} \Omega$
• C

  $6 \Omega$
• D

  $\frac{2}{3} \Omega$

Solution

In triangle formation, two resistors are in series and their sum is connected in parallel. Therefore,
$\begin{aligned} & R^{\prime}=2 \Omega+2 \Omega=4 \Omega \\ & \frac{1}{R^{\prime \prime}}=\frac{1}{4}+\frac{1}{2}=\frac{1+2}{4}=\frac{3}{4} \Omega \\ & R^{\prime \prime}=\frac{4}{3} \Omega\end{aligned}$

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