Question

Find the current in each resistor if R1 = 61, R2 = 41, R3 = 31, V1 = 18 V, V2 = 12 V, and V3 = 20 V. V1 R1 1 } R3 R2 V3 V2 +

Answer 1

ER, 1 IZ V2 as shown I , I₂ - Loop currents R,=64, R₂ =42, R3=32 į = 18 V, V2 = 12V, Vz=20V Apply KvL in loop 1 : I, R3+ (I, - Iz ) R₂=+V₂-v * I, x3 + (1,-1z) x 4 = 12-18 7 I, - 412 = -6 4 I-FI, = 6 o Apply kul in loop 2 : Iz Rit (Iz -I) R2=-V3 > Iz x 6+ (Iz-Iox 4 =-20 => 1012 - 4I, 2 - 20 -> 4I= 10 I2 + 20 > I, = 2.5 I2 + 5 From © and 4I2 - 7 (2.5 Izt 5) - 4 Iz 17.5 Iz -35=6 => -13.5 Iz = 41 =Y I2 = -3.037 A From I, = 2,5 (-3.037) +5 =- 2.592 A

3.037 A i current through resistor =1 Izl 3.037 current through resistor R2 = | I, - I2 / = | 2.592-(-3.037) = 70.445 current through resistor R₂ = 11,1=(2,592 A