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

In summary, the conversation discusses a circuit problem with given measured values and the use of Kirchhoff's Loop Rule and Junction Rule to solve it. The loop rule states that the sum of potential differences is zero around a loop, and the current flowing through resistors connected in series enters at one terminal and leaves at the other.
  • #1
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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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  • #2
Your I5 and I3, and also Io and I1 are related - how?

What does the Loop Rule state?
 
  • #3
The loop rule states that the sum of the potential differences around the circuit is 0. Is I3 = -I5? And also I1 = -Io?
 
  • #4
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?
 
  • #5


Kirchhoff's Rules, also known as Kirchhoff's Circuit Laws, are fundamental principles in circuit analysis that govern the behavior of electric circuits. These rules apply to circuits with multiple resistors in series, as well as circuits with other types of components.

Kirchhoff's Loop Rule, also known as Kirchhoff's Voltage Law, states that the sum of the voltage drops around a closed loop in a circuit must equal the sum of the voltage sources. This can be written as:

ΣV = 0

In the given circuit, there is only one closed loop, so this rule can be applied to find the voltage drop across each resistor. Starting from the top of the loop and moving clockwise, we have:

V - R1I1 - R2I2 - R3I3 - R4I4 - R5I5 = 0

Kirchhoff's Junction Rule, also known as Kirchhoff's Current Law, states that the sum of the currents entering a junction in a circuit must equal the sum of the currents leaving the junction. This can be written as:

ΣI = 0

In the given circuit, there are two junctions: one between R1 and R3, and one after R5. Applying this rule to each junction, we have:

At the first junction:
I1 = I2 + I3

At the second junction:
I5 + I2 = Io

Combining these equations with the loop rule, we can solve for the unknown currents and voltage drop across each resistor. Substituting the given values, we have:

V - R1(I2 + I3) - R2I2 - R3I3 - R4(I2 + I5) - R5I5 = 0

I1 = I2 + I3
I5 + I2 = Io

Solving these equations simultaneously, we get:
I1 = 0.01 A
I2 = 0.005 A
I3 = 0.005 A
I4 = 0.01 A
I5 = 0.005 A
Io = 0.01 A

Using Ohm's Law (V = IR), we can also calculate the voltage drop across each resistor:
VR1 = 1 V
VR2 = 0.5 V
VR3 = 0.5 V
VR4 = 1 V
VR5 =
 

1. What is Kirchhoff's Rule?

Kirchhoff's Rule, also known as Kirchhoff's Circuit Laws, are fundamental laws in circuit analysis that describe the behavior of current and voltage in an electrical circuit.

2. What are the two laws of Kirchhoff's Rule?

The two laws of Kirchhoff's Rule are Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). KCL states that the sum of currents entering a node in a circuit must equal the sum of currents leaving that node. KVL states that the sum of voltages around a closed loop in a circuit must equal zero.

3. When should Kirchhoff's Rule be used?

Kirchhoff's Rule should be used when analyzing complex circuits with multiple branches and nodes, as it allows for the calculation of unknown voltages and currents.

4. How do you apply Kirchhoff's Rule to a circuit?

To apply Kirchhoff's Rule, you must first identify all the nodes and branches in the circuit. Then, write out the equations for KCL and KVL for each node and loop in the circuit. Finally, solve the resulting system of equations to find the unknown currents and voltages.

5. Are there any limitations to Kirchhoff's Rule?

Kirchhoff's Rule assumes ideal circuit conditions, such as constant voltage sources and linear components. It also does not take into account factors such as parasitic resistance, capacitance, and inductance. Additionally, Kirchhoff's Rule is only applicable to DC circuits and not AC circuits.

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

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