Question

Find the potential difference across each resistor in the figure below. (R_1 = 4.90 Ohm, R_2 = 3.80 Ohm, R_3 = 2.80 Ohm, R_4 = 2.40 Ohm)

Answer 1

R3 + R4 = 5.2Ω

Picking all currents into junction. Incorrect currents will be negative.
KCL (top junction)
+ I1 + I2 + I34 = 0 (1)

KVL (left loop - ClockWise direction)
12 V - 4.9Ω I1 - 3 V + 3.8Ω I2 = 0 (2)
9 + 3.8 I2 = 4.9 I1
I1 = 1.875 + 0.775 I2 (2A)

KVL (right loop - ClockWise direction)
-3.8Ω I2 + 3 V + 5.2Ω I34 - 18 V = 0 (3)
5.2 I34 = 15 + 3.8 I2
I34 =2.88+.730(3A)

Substitute 2A and 3A into 1.

+ I1 + I2 + I34 = 0
( 1.875 + 0.775 I2 ) + I2 + ( 2.88+ 0.73 I2 ) = 0
-4.755 = 2.505I2
I2 = -1.898A

Solve 2A and 3A for other currents.

I1 = 1.875 + 0.775 I2 = 1.875 -.775* 1.898 = 0.404 A
I34 = 2.88+.730I2= 3.409 + 0.730 * -1.898 = 2.02 A

V1 = I1 R1 = 0.404A * 4.90Ω = 1.98V
V2 = I2 R2 = 1.898A * 3.80Ω = 7.21V
V3 = I34 R3 = 2.02A * 2.80Ω = 5.656V
V4 = I34 R4 = 2.02A * 2.40Ω = 4.848V