Applying Kirchoff's Voltage Law to a circuit

In summary, Kirchhoff's rules were used to find the currents in three resistors, and the potential difference between points c and f was found.
  • #1
David Day
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1

Homework Statement



Using Kirchhoff’s rules, (a) find the current in each
resistor shown in Figure P28.31 and (b) find the potential
difference between points c and f.
upload_2018-7-30_23-8-27.png
[/B]

Homework Equations


[/B]
Σ ΔV = 0 (KVL)

The Attempt at a Solution


[/B]
I have been trying to set up a system of equations for the three loops as shown in the picture, but I can't seem to get the right numbers. I was able to get the currents using mesh-current analysis; they are 0.38 mA, 3.08 mA, and 2.69 mA for resistors 1, 2 and 3, respectively. However, I would like to know what mistake I'm making in applying basic KVL to the loops. The equations I get for each loop are:

L1: 70V - 60V - V2 - V1 = 0

L2: 60V - V3 - 80V + V2 = 0

L3: 70V - V3 - 80V - V1 = 0

where V1, V2, and V3 correspond to the voltages at R1, R2, and R3, respectively.

One issue I have noted but am unsure of is whether or not V2 in the second equation should be positive or negative. If I assume the current is flowing downward across R2 it is negative in equation 1. Therefore, I should continue to assume current is flowing downward across R2, which would mean V2 is positive for equation 2. Is that correct?

Any help would be greatly appreciated!

EDIT:

I see now that my equations are not providing enough information to solve for the variables. If I solve for V3 in equation 3 and plug that into equation 2, my equation 2 is just the same equation 1. I'm not sure where to go from this point...

EDIT:

I found my problem. I was missing an equation, I1 = I2 + I3. Using this to solve the system of equation yields the correct results.
 

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  • #2
David Day said:
One issue I have noted but am unsure of is whether or not V2 in the second equation should be positive or negative. If I assume the current is flowing downward across R2 it is negative in equation 1. Therefore, I should continue to assume current is flowing downward across R2, which would mean V2 is positive for equation 2. Is that correct?
Yes, that's right.
 
  • #3
David Day said:
One issue I have noted but am unsure of is whether or not V2 in the second equation should be positive or negative.

You have it right but it's good practice to mark voltage arrows on the circuit before starting to write the equations.
 
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  • #4
David Day said:
I found my problem. I was missing an equation, I1 = I2 + I3. Using this to solve the system of equation yields the correct results.
Yup, that's a KCL equation. It might be useful to note that this problem can be solved by writing just one equation using the analysis method based on KCL called nodal analysis. Since the problem has been solved by the OP and it's been several weeks, I can offer up this alternative approach.

Choose node ##f## as the common reference point and write the node equation for node ##c## :
upload_2018-9-26_10-26-29.png


$$\frac{V_c - 70}{2000} + \frac{V_c - 60}{3000} + \frac{V_c - 80}{4000} = 0$$
Each of the terms in the node equation represents a current leaving the node by one of the node branches (i.e. KCL for the node).

Then just solve for ##V_c##, which will be the potential at node ##c## with respect to node ##f##.
 

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Related to Applying Kirchoff's Voltage Law to a circuit

1. What is Kirchoff's Voltage Law?

Kirchoff's Voltage Law, also known as KVL, is a fundamental law in circuit analysis that states that the algebraic sum of all voltages in a closed loop is equal to zero. This means that in any closed loop, the voltage drops and rises must balance out.

2. How is Kirchoff's Voltage Law applied to a circuit?

KVL is applied to a circuit by analyzing the voltage drops and rises across each element in a closed loop and writing them in a mathematical equation. This equation is then solved for the unknown voltages in the circuit.

3. What are the assumptions made when applying Kirchoff's Voltage Law?

The main assumptions made when applying KVL are that the circuit is in a steady state, all components are ideal, and that the circuit is a closed loop with no branches or nodes. Additionally, the voltage sources in the circuit must be independent.

4. Can Kirchoff's Voltage Law be applied to any circuit?

Yes, KVL can be applied to any circuit, regardless of its complexity. However, for more complex circuits, it may be easier to break them down into smaller loops and apply KVL to each loop separately.

5. What is the significance of Kirchoff's Voltage Law in circuit analysis?

KVL is a fundamental law that allows us to determine the voltages in a circuit without having to measure each voltage individually. It is an important tool in circuit analysis and is used to calculate the voltage across each element in a closed loop circuit.

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