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 V_{1} = 2V and V_{2} = 10V respectively. The magnitude of the resistances is R_{1} = 2Ω; R_{2}Ω = 2; and R_{3} = 3Ω. Calculate the magnitude and direction of the current across the resistor R_{2}.

**2. Relevant equations**

Kirchhoff’s junction and loop rule.

**3. The attempt at a solution**

I_{1} = I_{2} + I_{3} (JR)

v_{1} – I_{1}R_{1} – I_{2}R_{2} = 0 (loop A)

-I_{3}R_{3} + V_{2} + I_{2}R_{2} = 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,

BOAS

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