Question

In the circuit shown, the current in the 1$\Omega$ resistor is :

• A. 1.3 A, from P to Q
• B. 0 A
• C. 0.13 A, from Q to P
• D. 0.13 A, from P to Q

Answer 1

The correct option is C 0.13 A, from Q to P

$\text{Step 1 : Applying KVL in loop 1}$

$9-2i-1(i-i_1)-3i=0$

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

$\text{Step 2 : Applying KVL in loop 2}$

$6-3i_1+1(i-i_1)=0$

$\Rightarrow -i+4i_1=6$ $...\left(2\right)$

$\text{Step 3 : Solving equations (1) and (2)}$

Eq $\left(1\right)\times 4+$ Eq$\left(2\right)$

$\Rightarrow 23i=42$

$\Rightarrow i=1.826A$

Put the values of $i$ in equation $\left(1\right)$

$\Rightarrow 6\times 1.826-i_1=9$

$\Rightarrow i_1=1.956A$

Current through 1$\Omega$ resistor $=i-i_1=-0.13A$
Therefore, current through 1$\Omega$ resistor is $0.13A$ from Q to P

Hence, Option (C) is correct.