Using the information from the following circuit, answer the related questions a

Question

Using the information from the following circuit, answer the related questions and ultimately calculate all three currents; I_1, I_2, I_3. The battery emf's are:. epsilon_1 = 19 V epsilon_2 = 6 V epsilon_3 = 2 V The resistors are : R_1 = 6 Ohm R_2 = 4 Ohm R_3 = 4 Ohm R_4 = 1 Ohm According to Kirchhoff's current rule, the current equation for joint "a" will be: According to Kirchhoffs voltage rules, circle the equation corresponding to the inside of the left loop. Last using Kirchhoffs voltage and current rules calculate all three currents in the circuital.

Explanation / Answer

here,

According to KCL , the current equation for joint a

I1 = I2 + I3 ...(1)

according to KVL,

for the left loop

R1 * I1 + R4 * I3 + R2*I1 + E3 - E1 = 0

or

E1 - I1*R1 - I3*R3 - E3 - I1*R2 = 0

19 - 6*I1 - 4*I3 - 2 - 4*I2 = 0 ....(2)

According to KVL,

for the right loop

R3*I2 + E2 - E3 - R4*I3 = 0

4*I2 + 6 - 2 - 1 * I3 = 0 .....(3)

from (1), (2) and (3)

I1 = 1.7 A

I2 = - 0.46 A

I3 = 2.16 A

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