Question

In the circuit shown, potential difference between points $\text{A}$ and $\text{B}$ is $16\text{V}$. The current passing through $2\Omega$ resistor will be

• A. Zero
• B. $2.5\text{A}$
• C. $3.5\text{A}$
• D. $4\text{A}$

Answer 1

The correct option is C $3.5\text{A}$


Let the current passing through the $2\Omega$ resistor be $i_1$.

Using, $\text{KCL}$ let us find the Potential differnce between points $\text{A}$ and $\text{B}$

$V_A-4i-9-(i-i_1)+3-4i=V_B$

$\Rightarrow V_A-V_B=4i+9+i-i_1-3+4i$

$\Rightarrow 16=9i-i_1+6$
$9i-i_1=10...\left(1\right)$

For the loop $MNOPM$, Using $\text{KVL}$

$-9-(i-i_1)+2i_1=0$

$3i_1-i=9...\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$ , $26i_1=91$
$i_1=\frac{91}{26}=3.5\text{A}$

Hence, option (c) is the correct answer.