Question

In the following circuit, if potential difference between $A$ and $B$ is $V_{AB}=4V$ , then the value of $X$ will be

• A. $5\Omega$
• B. $10\Omega$
• C. $15\Omega$
• D. $20\Omega$

Answer 1

Answer: (D)

In the circuit $10\Omega$ and $X\Omega$ resistance are in series combination.
Thus, $R=10+X$
From the circuit diagram,
Current, $i=\frac{E}{R}$
$=\frac{5-2}{10+X}=\frac{3}{10+X}$
We know that
$V_{AB}=E+ir$
[$\because$ because current flows from positive terminal to negative terminal]
Here, $V_{AB}=4V$
$4=2+\frac{3}{10+X}\times X$
$2=\frac{3X}{10+X}$
$2(10+X)=3X$
$20+2X=3X$
$X=20\Omega$