Question

In the following circuit if $V_A-V_B=4\text{V}$, then the value of resistance $X$ in $\text{ohms}$ will be:

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

Answer 1

The correct option is D $20$


Applying $\text{KVL}$ in the circuit (entire loop),

$+5-10i-2-Xi=0$

$(10+X)i=3......\left(1\right)$

And given that

$V_A-V_B=4\text{V}$

Again apply $\text{KVL}$ from $A\to B$

$\therefore V_A-2-iX=V_B$

$V_A-V_B=2+iX=4$

$\therefore iX=2....\left(2\right)$

Putting the value in equation $\left(1\right)$,

$10i+2=3\Rightarrow i=\frac{1}{10}\text{A}$

From eq. $\left(2\right)$, we get

$\frac{1}{10}X=2$

$\therefore X=20\Omega$

Why this problem ? It involves a detailed understanding of $\text{KVL}$ in the circuit.