Find all the currents flowing in the circuit shown using Kirchhoff’s loop and ju

Question

Find all the currents flowing in the circuit shown using Kirchhoff’s loop and junction rules. Report the magnitude of I2. (answer in Amps)

Keep extra digits of precision in all calculations (more than the required sig figs until the very end when reporting the final value for I2)

Before attempting this problem review and understand the example/solution given at the end of lecture 7. Lecture slides are posted on KSOL and Top Hat.

Note the direction of currents have already been guessed for you, use those directions (who know if those are the actual directions, it is just better if we all have the same directions for collaborations sake and working together in your homework groups). Also, remember if you “walk” around the circuit in the opposite direction of one of your peers, a negative sign will simply be multiplied through your loop equations.

Explanation / Answer

Here I3 = I1 + I2
Now considering the loop 1
5I1 -24 +0.1I1 +20I1 +(I1 -I3)40 + (I1 -I3)0.5 + 48 = 0
65.6 I1 - 40.5 I3 = -24 -----------------(1)
Now for loop 2
(I3 - I1)(40.5) -48 + 0.2I3 +36 + 0.05I3 -6 +78I3 = 0
118.75 I3 - 40.5 I1 = 54 --------------(2)
Solving avobe equation
we get I1 = - 0.534 A , I2 = 0.27256 A
I3 = -0.534 + 0.27256 = -0.26144 A

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