Question

Given the Circuit below: V1 R1 200 Ω 200 V R2 500 Ω R3 400 Ω V2 R4 300 Ω 400 V Calculate the Currents (Ii, I2, I5, 14) through each resistor

Answer 1

since R₂ and R₃ are in parallel

i₂ R₂ = i₃ R₃

i₂ (500) = i₃ (400)

i₃ = 1.25 i₂

using KCL :

i₁ + i₄ = i₂ + i₃

i₁ + i₄ = 1.25 i₂ + i₂

i₁ + i₄ = 2.25 i₂                                          eq-1

using KVL in loop ABCHA

i₁ R₁ - V₁ + i₂ R₂ = 0

200 i₁- 200 + 500 i₂ = 0

i₁= (200 - 500 i₂ )/200                                            eq-2

using KVL in loop EDGFE

i₃ R₃ - V₂ + i₄ R₄ = 0

400 i₃- 400 + 300 i₄ = 0

i₄ = (400 - 400 i₃ )/300                                                    eq-3

using eq-1 , eq-2 and eq-3

(200 - 500 i₂ )/200 + (400 - 400 i₃ )/300 = 2.25 i₂  

(200 - 500 i₂ )/200 + (400 - (400) (1.25) i₂)/300 = 2.25 i₂  

i₂ = 0.364 A

i₃ = 1.25 i₂ = 1.25 x 0.364 = 0.455 A

i₁= (200 - 500 i₂ )/200 = (200 - 500 (0.364))/200 = 0.09 A

i₄ = (400 - 400 i₃ )/300   = (400 - 400 (0.455))/300 = 0.727 A