Using Kirchoff's Loop Rule to Determine Currents in a Circuit

[JessicaHelena]

Homework Statement

Homework Equations

Kirchoff's Rule
The sum of all V = 0

The Attempt at a Solution

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I think I'm having a problem determining the current at r_2 and R_3. I had originally thought the currents at both resistors would be I_3, writing E_2 — r_2 I_3 — R_3 I_3 — I_1 R_1 = 0, but I got it wrong, so I thought that the current at both must've been I_1, getting the answer as screenshotted above, but that is wrong as well...

 

[gneill]

I think I'm having a problem determining the current at r_2 and R_3. I had originally thought the currents at both resistors would be I_3, writing E_2 — r_2 I_3 — R_3 I_3 — I_1 R_1 = 0, but I got it wrong, so I thought that the current at both must've been I_1, getting the answer as screenshotted above, but that is wrong as well...

You are correct that the current through ##r_2## and ##R_3## is ##I_3## ; they are in series and only ##I_3## is in that branch of the circuit. Your answer in the above quote looks okay to me. Are there any special rules regarding the answer formatting that you might have overlooked? For example, do you need to enter a complete equation (with an equals sign), or group like current terms ( writing ##-~(r_2 + R_3)I_3## rather than ##-~r_2 I_3 - R_3 I_3## )?

 

[CWatters]

The problem statement says "Apply the loop rule to loop aefgha". So my guess is they expect you to start at node "a" and go clockwise. So the first term would be +I₁R₁. The plus sign is optional.