Question

Calculate the currents in the following circuit.

Answer 1

Applying Kirchoff’s 1^st Law at junction B

I₁ – I₁ – I₃ = 0

I₃ = I₁ – I₂ …… (1)

Applying Kirchoff’s II^nd Law at junction in ABEFA

100 I₃ + 100 I₁ = 15

100 (I₃ + I₁) = 15

100 I₁ – 100 I₂ + 100 I₁ =15

200 I₁ – 100 I₂ = 15 …… (2)

Applying Kirchoff’s IInd Law at junction in BCDED

- 100I₂ + 100 I₃ = 9

- 100 I₂+ 100(I₁ – I₂) = 9

100I₁ – 200 I₂ = 9

Solving equating (2) and (3)

equ. (2) × 2

400 I₁ - 200 I₂ = 30
100 I₁ - 200 I₂ = 9
(-)      (+)          (-)  
   300 I₁ = 21
    I₁ = 0.07 A

Substitute I₁ values in equ (2)

200(0.07) – 100 I₂ = 15

14 – 100 I₂ = 15

– 100 I₂ = 15 – 14

I₂ = −1100

I₂ = -0.01A

Substitute I₁ and I₂ value in equ (1), we get

I₃ = I₁ – I₂ = 0.07 – (-0.01)

I₃ = 0.08 A.