Question

M w R6 V1 w R7 For the circuit in the figure above, Vi=12 V. Ri=50, R2 = 10 . R3 = 8 0 R4 = 2 0 Rs=3 R6 = 70, and Ry=90. What are the currents through and potentials across each of the resistors?

Answer 1

from the circuit

r4 and r5 are in parallel

r45 = 2*3/(2+3) = 1.2 ohm

r6 and r7 are also in parallel

r67 = 7*9/(7+9) = 3.94 ohm

r2 and r45 are in series

r245 = 1.2+10 = 11.2 ohm

r3 and r67 are in series

r367 = 3.94+8 = 11.94 ohm

r245 and r367 are in parallel

r234567 = 11.2*11.94/(11.2+11.94) = 5.78 ohm

r1 and r234567 are in series

r tot = 5+5.78 = 10.78 ohm

total current i tot = 12/10.78 = 1.113 A

current across r1 = 1.113 A

voltage across r1 is v1 = 1.113*5 = 5.565 V

i234567 = 1.113 A

v234567 = 12-5.565 = 6.435 V

in parallel voltage is same and in series current is same

v245 = v367 = 6.435 V

i245 = 6.435/11.2 = 0.575 A

i2 = 0.575 A

v2 = 0.575*10 = 5.75 V

i45 = 0.575 A

v45 = 0.575*1.2 = 0.69 V

v4 = v5 = 0.69 V

i4 = 0.69/2 = 0.345 A

i5 = 0.69/3 = 0.23 A

i367 = 6.435/11.94 = 0.539 A

i3 = 0.539 A

v3 = 0.539*8 = 4.312 V

i67 = 0.539 A

v67 = 0.539*3.94 = 2.123V

v6 = v7 = 2.123 V

i6 = 2.123/7 = 0.303 A

i7 = 2.123/9 = 0.236 A