In the circuit shown in the figure, R 1 = 5.13 ?, R 2 = 10.7 ?, and R 3 = 15.1 ?
ID: 2242711 • Letter: I
Question
In the circuit shown in the figure, R1 = 5.13 ?, R2 = 10.7 ?, and R3 = 15.1 ?, Vemf,1 = 11.5 V, and Vemf,2 = 15.5 V. Using Kirchhoff's Loop and Junction Rules, determine the following currents:
a) Current i1 flowing through resistor R1 in the direction indicated in the figure.
b) Current i2 flowing through resistor R2 in the direction indicated in the figure.
c) Current i3 flowing through resistor R3 in the direction indicated in the figure.
please write a b and c clearly
In the circuit shown in the figure, R1 = 5.13 ?, R2 = 10.7 ?, and R3 = 15.1 ?, Vemf,1 = 11.5 V, and Vemf,2 = 15.5 V. Using Kirchhoff's Loop and Junction Rules, determine the following currents: Current i1 flowing through resistor R1 in the direction indicated in the figure. Current i2 flowing through resistor R2 in the direction indicated in the figure. Current i3 flowing through resistor R3 in the direction indicated in the figure.Explanation / Answer
apply KVL in upper loop
i1*R1 - V1 - i2*R2 + V2 = 0
i1*R1 - i2*R2 = V1-V2
5.13*i1 - 10.7*i2 = -4 --(1)
apply KVL in lower loop
i3*R3 - V2 + i2*R2 = 0
i3*R3 + i2*R2 = V2
10.7*i2 + 15.1*i3 = 15.5 --(2)
and, i1 + i2 = i3
substitute i3 in eqn (2)
10.7*i2 + 15.1*(i1+i2) = 15.5
15.1*i1 + 25.8*i2 = 15.5 --(3)
25.8*eqn(1) + 10.7*eqn(3)
==> 25.8*5.13*i1 + 15.1*10.7*i1 = -4*25.8 + 10.7*15.5
==> 293.924*i1 = 62.65
==> i1 = 62.65/293.924
==> i1 = 0.213 A
from eqn(3)
15.1*0.213 + 25.8*i2 = 15.5
i2 = (15.5 - 15.1*0.213)/25.8
i2 = 0.476 A
i3 = i1+i2
= 0.689 A