In the circuit shown in the figure, find the current flowing through the 12 Ω resistor.

The correct answer is option 4):(0.75 A)

Concept:

KVL states that algebric sum of the  all voltage differences around any closed loop is zero.

Calculation:

Given

The I₁ be the current in the loop 1,The I₂ be the current in the loop 2

KVL at Loop  1

36 - 3 I₁ - 12(I₁ - I₂) = 0

KVL at Loop  2

24 - 4 I₂ - 12 (I1 - I2) = 0

36 - 3 I1 - 12 I₁ + 12 I₂ = 0

36 - 15 I1 + 12 I2 = 0

5I1 - 4 I2 = 12 ------------(1)

24 - 4 I2 - 12 (I₁ - I₂) = 0

24 - 4 I2 - 12 I1 +  12  I2 = 0

3 I1 - 4I2 = -6------------------(2)

solving  1 and 2 we get

I₁ = 9 A

I₂ = 8.25

The current across 12 Ω resistor is

I₁ - I₂ = 0.75 A