Kirchhoff’s Rules


i’m stuck on this problem and have been trying to identify where I might have made an error but have come up empty. I have assigned my loops and junctions and have three equation for three unknowns, but can’t seem to solve them…

1. The problem statement, all variables and given/known data

Consider the circuit in the following diagram (attached):

where the two ideal dc batteries deliver a terminal voltage of V1 = 2V and V2 = 10V respectively. The magnitude of the resistances is R1 = 2Ω; R2Ω = 2; and R3 = 3Ω. Calculate the magnitude and direction of the current across the resistor R2.

2. Relevant equations

Kirchhoff’s junction and loop rule.

3. The attempt at a solution

I1 = I2 + I3 (JR)

v1 – I1R1 – I2R2 = 0 (loop A)

-I3R3 + V2 + I2R2 = 0 (loop B)

I can’t see how to solve for any of these, which is making me think i’ve worked out the expressions wrong, but I cant find the mistake.

Thanks for any help you can give,


Attached Images
File Type: png kirchhoff.PNG (14.6 KB)

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