Question

In the following circuit diagram the value of resistance X for the potential difference between B and D is zero :-

• A. 4 ohm
• B. 6 ohm
• C. 8 ohm
• D. 9 ohm

Answer 1

The correct option is C 8 ohm

As potential between B and D is zero so it is a balanced Wheatstone bridge circuit, i.e. $P/Q=R/S$
Here, $P=15+6=21,Q=\left(8||X\right)+3=\frac{8X}{8+X}+3=\frac{11X+24}{8+X}$,

$R=15+\left(6||6\right)=15+6/2=18,S=4+\left(4||4\right)=4+4/2=6$
Thus, $\frac{21(8+X)}{11X+24}=\frac{18}{6}=3$
or $33X+72=168+21X$
or $12X=96$
$X=8\Omega$