- #1

joel amos

- 104

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Ω

In the following circuit, what is the current across the R

V

Kirchhoff's laws

I attempted to create a system of equations with the intention of finding R

Node A: I

Loop 1: 1.5 V - I

Loop 2: I

V

I've now expressed I

I

However, I realized that I don't have enough equations to use to solve this system of equations for I

## Homework Statement

In the following circuit, what is the current across the R

_{2}resistor?V

_{1}= 1.5 V, V_{2}= 1.5 V, R_{1}= 470 Ω, R_{2}= 560 Ω## Homework Equations

Kirchhoff's laws

## The Attempt at a Solution

I attempted to create a system of equations with the intention of finding R

_{2}, as was demonstrated in an example in class. Here are my equations:Node A: I

_{2}= I_{1}+ I_{3}Loop 1: 1.5 V - I

_{1}* 470 Ω - I_{2}* 560 Ω = 0Loop 2: I

_{2}* 560 Ω - 1.5 V = 0V

_{1}- I_{1}* R_{1}- I_{2}* R_{2}= 0 ⇒I_{1}* R_{1}= V - I_{2}* R_{2}⇒ (V_{1}- I_{2}* R_{2}) / R_{1}= (1.5 V - I_{2}* 560 Ω) / 470 Ω = I_{1}I've now expressed I

_{1}in terms of I_{2}. So I can write:I

_{2}= [(1.5 V - I_{2}* 560 Ω) / 470 Ω] + I_{3}However, I realized that I don't have enough equations to use to solve this system of equations for I

_{2}. In class we created a third loop that went around the whole outside. However, would that be possible in this case, as that isn't a path of current? And even if I were to add a third loop, I can't see how that'd help my cause.
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