Four resistors, $100 \Omega, 200 \Omega, 300 \Omega$ and $400 \Omega$ are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square?

• A

  $210 \Omega$
• B

  $240 \Omega$
• C

  $300 \Omega$
• Correct answer
  D

  $250 \Omega$

Solution

For maximum equivalent resistance across the diagonal of the square, the given resistors connected as Resistance of $P Q R$ arm, $R_{1}=300+200=500 \Omega$ Resistance of $P S R$ arm, $R_{2}=400+100 \Omega=500 \Omega$ The equivalent resistance between $P$ and $R$. $$ \begin{aligned} \frac{1}{R_{e q}} &=\frac{1}{R_{1}}+\frac{1}{R_{2}} \\ &=\frac{1}{500}+\frac{1}{500}=\frac{1+1}{500} \\ \therefore \quad R_{e q} &=\frac{500}{2}=250 \Omega \end{aligned} $$

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