Emf1 has the value 12.1, Emf2 has the value 12.0. Resistor R1 has the value 33.0

Question

Emf1 has the value 12.1, Emf2 has the value 12.0. Resistor R1 has the value 33.0, resistor R2 has the value 50.0 and R3 has the value 24.0.

Find the current in resistor R2, taking current going to the right to be to be positive.

Current in R2:

ind the current in resistor R3, taking current going to the right to be to be positive.
Current in R3:
Find the current in resistor R1, taking current going downward to be to be positive.
Current in R1:

im just not sure how to do this. i know i can solve currents i_A and i_B. once i solve for those do i do the V/I=R ?

Explanation / Answer

Use Kirchhoff's Rules

I2 = I1 + 13

E1 - I1R1 - I2R2 = 0

E2 +I1R1 - I3R3 = 0 or 12 = 33I1 - 24

I3 I3 = (12 - 33I1)/-24

From the second equation, we can say

E1 - I1R1 - I1R2 - I3R2 = 0 or 12.1 - 33I1 - 50I1 - 50I3 = 0

12.1 - 83I1 -50I3 = 0

then 12.1 - 83I1 - (50)((12 - 33I1)/-24 = 0

12.1 - 83I1 +25 - 68.75I1 = 0

37.1 = 151.75 I1

I1 = .244 A

Substitute back into 12.1 - 83I1 -50I3 = 0 to find I3

12.1 - (83)(.244) - 50I3 = 0

-8.152 = 50I3

I3 = -.163 A

Finally use I2 = I1 + 13 to find I2

so I2 = .244 - .163

I2 = .081 A

So the current going through R2 = .081 A

Current going through R3 = -.163 A

Current going through R1 = .244 A

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