Question

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. $300\, \Omega$
• D. $250 \,\Omega$

Answer 1

Answer: (D)

For maximum equivalent resistance across the diagonal of the square, the given resistors connected as

Resistance of $PQR$ arm, $R_{1}=300+200=500 \,\Omega$
Resistance of $PSR$ arm, $R_{2}=400+100\, \Omega=500 \,\Omega$
The equivalent resistance between $P$ and $R$.
$\frac{1}{R_{\text {eq }}} =\frac{1}{R_{1}}+\frac{1}{R_{2}} $
$=\frac{1}{500}+\frac{1}{500}=\frac{1+1}{500} $
$\therefore R_{\text {eq }}=\frac{500}{2}$
$=250 \,\Omega$