- #1
joel amos
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Ω
In the following circuit, what is the current across the R2 resistor?
V1 = 1.5 V, V2 = 1.5 V, R1 = 470 Ω, R2 = 560 Ω
Kirchhoff's laws
I attempted to create a system of equations with the intention of finding R2, as was demonstrated in an example in class. Here are my equations:
Node A: I2 = I1 + I3
Loop 1: 1.5 V - I1 * 470 Ω - I2 * 560 Ω = 0
Loop 2: I2 * 560 Ω - 1.5 V = 0
V1 - I1 * R1 - I2 * R2 = 0 ⇒I1 * R1 = V - I2 * R2 ⇒ (V1 - I2 * R2) / R1 = (1.5 V - I2 * 560 Ω) / 470 Ω = I1
I've now expressed I1 in terms of I2. So I can write:
I2 = [(1.5 V - I2 * 560 Ω) / 470 Ω] + I3
However, I realized that I don't have enough equations to use to solve this system of equations for I2. 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.
Homework Statement
In the following circuit, what is the current across the R2 resistor?
V1 = 1.5 V, V2 = 1.5 V, R1 = 470 Ω, R2 = 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 R2, as was demonstrated in an example in class. Here are my equations:
Node A: I2 = I1 + I3
Loop 1: 1.5 V - I1 * 470 Ω - I2 * 560 Ω = 0
Loop 2: I2 * 560 Ω - 1.5 V = 0
V1 - I1 * R1 - I2 * R2 = 0 ⇒I1 * R1 = V - I2 * R2 ⇒ (V1 - I2 * R2) / R1 = (1.5 V - I2 * 560 Ω) / 470 Ω = I1
I've now expressed I1 in terms of I2. So I can write:
I2 = [(1.5 V - I2 * 560 Ω) / 470 Ω] + I3
However, I realized that I don't have enough equations to use to solve this system of equations for I2. 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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