How do Kirchhoff's Rules apply to a circuit with multiple resistors in series?

AI Thread Summary
Kirchhoff's Rules apply to circuits with multiple resistors in series by using the Junction Rule and Loop Rule to analyze current and voltage. The Junction Rule indicates that the sum of currents entering a junction equals the sum of currents leaving, while the Loop Rule states that the sum of potential differences around any closed loop in the circuit must equal zero. In the given circuit, the relationships between currents I1, I2, I3, I5, and Io need to be established to solve for unknowns. The discussion raises questions about how currents interact at junctions and through resistors, emphasizing that current remains constant in series circuits. Understanding these principles is crucial for correctly applying Kirchhoff's Rules to analyze the circuit.
Sylvia
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Homework Statement


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Consider the circuit above. You are given the following measured values:
V = 1.5 V
R1 = 100
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R2 = 100
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R3 = 50
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R4 = 50
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R5 = 50
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Homework Equations


Kirchhoff's Loop Rule and Junction Rule

The Attempt at a Solution



I tried setting this up using the junction and loop rule.
At the first junction (between R1 and R3), I have I1 = I2 + I3. At the second junction, after R5, I have I5 + I2 = Io (Io is the current entering the battery again).
I do not understand what the loop rule should be written as and then how to put it all together. Please help!
 
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Your I5 and I3, and also Io and I1 are related - how?

What does the Loop Rule state?
 
The loop rule states that the sum of the potential differences around the circuit is 0. Is I3 = -I5? And also I1 = -Io?
 
Sylvia said:
The loop rule states that the sum of the potential differences around the circuit is 0. Is I3 = -I5? And also I1 = -Io?
The loop rule states that the sum of potential differences is zero around a loop.

I3 = - I5 would mean that the current flows into R4 from both sides and the charges accumulate there. Is it possible? The current flows through a resistor, enters at one terminal and leaves at the other. What do you know about the current flowing through resistors connected in series?
 
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