Question

From the circuit shown below,

a M 10 V 30 il 222 i2 722 892 i3 12 V W

(a) use KCL and KVL to solve for the three currents.

(b) With the given data below and the two currents flowing clockwise, determine both currents using mesh analysis and the voltages across each resistor.

r1= 3 Ohms

r2= 7 Ohms

r3= 2 Ohms

r4= 8 Ohms

Answer 1

ΤΟΥ a LI s (a) By KCL,. Vat 10 M 31 an + Vat Va-12 20 8 2 7 + 3 81 mu 2.3 12 V ov, Yal? + + + + + 2) = (1 - 1) . 0.725va = -0.05 i. Va = -0.069 volt. .. Va - 12 0.069 - 12 A AS - 1.20694 10 3 + 7 12 = va : -6.069 A - 0.0345A 2 = Vario - 0.069+10 A = 1.241375 A : 8 iz negative sign denotes the current is flowing direction to the direction taken in the cirmit. in opposite . Circuit with Correct direction 107 1:1-20 69 A in 0.03451 iz Y1-2413754 212 MH thier

10V. + 30 312 B) By 0 (2) FO Vat By KVL in loop di 10 + 2 (5-५) + 81320 5 +i -i ++i320 14 =_51, +5 ------ 22 7/- 8.2 + 121 ४

e By KVL in loop , 12 1 12 + 1014 + 2(14-1₂)=0 6+514 + 14 13 il Or, 6+614 -13 we know; in a 513 + 5 6+ 6( 5i3+5) - 3-0 oy, 6+ 3013 + 30-32 291, 2-36 :: lz =-1•2413A .. 14:56-1-2413) +5 A = -19069. A. :. Current through su resistors i = -1.2413 A Current through Fr and 3r resistor = '4 =-1-20694 ar resistor 13-14 =4-2413 + 1.2069)A =-0.0344 A . OY 2 3 4 current through 5 6 .. Voltage accross &r ; Ver = siz = -12413x8 V-9.93041 Voltage accross Frig Vani = 714 5-7 X1•2069V=-8.4483 V 35; Var = 3/4 = -3X1-2069V = -3.62071 20; Vzur =-2 (13-14) --2*0.0344V =-0.0688V 19