Question

Find equations using Kirchhoffs laws to solve the currents in each branch of the following circuit. Show all the important steps required in finding the equations. Solve the equations to calculate the currents.You are allowed to use any valid method to solve the equations.Consider ε₁ = 20 V, ε₂ = 10.0 V, ε₃ = 20 V, R₁ = 4.0 Ω, R₂ = 10.0 Ω, R₃ = 10.0 Ω, R₄ = 4.0 Ω.

R4 ww R2 E & E2 w w R3 R

Answer 1

b to Ry R₂ sun E2 Iz R₃ at the junction a RA umy Ii I, Appling kinchhof's cunnent law the get, I,+I3 = I2 > kirchhof's voltage to the loo 10op Ig Rq + I, R, = 6,-E2 ar 4 Is + 10 I2 21, +5 I2 = 5 Applying law a b c da cueget, 20-10 Againg applying kinchhoft's voltage law to the loop als fea [using Equ we = 10 we get, Iz R2 +I3 (R3 +Rq) = E3-E2 m 10 I2 + Iz (10+4) = 20-10 ar 10 I2 + 14 ( IL - I,) = 10 24 72 – 14 I, = 10 12 12 - 71, = 5 (3) E912) X7+ + Eq 3) x2 get, 141, + 39 19 = 35 - 141, +24 I 2 = +59 I2 = 45 Iq = 0.76 A Use the value of Iz in Eg(2) we get, 2 I, = 5-10 x 0.7 0.75) I, -0.6A use the value of I, & Iz in Eg (1) we Iz = I2 -1, = (0.76 0.6) A Iz = 0.16 A CSScanned with CamScanner O get,