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, $V_{AB} = 4\,V$
$ 4 = 2+ \frac{3}{10 + X} \times X$
$ 2 = \frac{3X}{10 + X}$
$2(10 + X) = 3X$
$ 20 + 2X = 3X$
$X = 20 \,\Omega$