Question

Four conductors of the same resistance are connected to form a square. If the resistance between diagonally opposite corners is $8\Omega$, the resistance between any two adjacent corners would be _____.

• A. $32\Omega$
• B. $8\Omega$
• C. $\frac{1}{6}\Omega$
• D. $6\Omega$

Answer 1

The correct option is D $6\Omega$

As shown in the figure below, $R$ is the resistance of a side of the square.


Given, the resistance along a diagonal, say AD, is $R_d=8\Omega$
The effective resistance between A and D is also equal to
$R_{eff}=R_{ABD}||R_{ACD}$
where $R_{ABD}$ = Resistance along the path ABD = $2R$ = Resistance along the path ACD = $R_{ACD}$.
$⟹R_{eff}=\frac{2R\times 2R}{2R+2R}=R=8\Omega$
Hence, the value or R is 8 $\Omega$.
Now, resistance between any two adjacent sides, say A and C, can be calculated as follows:
$R_{AC,eff}=R_{AC}||R_{ABDC}=\frac{R\times 3R}{R+3R}$ = $\frac{3R}{4}=\frac{3\times 8}{4}=6\Omega$.