Kirchhoff's Loop Rule Conceptual Question

In summary, the circuit shown consists of four resistors and a battery, with unknown values. The expressions equal to the voltage of the battery are V_A + V_B + V_C + V_D. However, there are two possible solutions according to Kirchhoff's voltage rule, which states that the sum of all voltages in a closed loop is equal to zero. By applying this law to one of the closed loops, it is possible to find the voltage across the battery, represented as V_bat. The loop can be divided into two paths, and the sum of the voltages for both paths must be equal. Therefore, the sum of V_A and V_B is equal to the voltage across the battery. There are three possible paths
  • #1
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Homework Statement



The circuit shown below consists of four different resistors and a battery. You don't know the strength of the battery or the value any of the four resistances.

1011455.jpg


Select the expressions that will be equal to the voltage of the battery in the circuit, where [tex]V_{A}[/tex], for example, is the potential drop across resistor A.

[tex]V_{A} + V_{B}[/tex]
[tex]V_{B} + V_{C}[/tex]
[tex]V_{B} + V_{C}[/tex]
[tex]V_{A} + V_{B}+ V_{C}[/tex]
[tex]V_{A} + V_{B} + V_{C} + V_{D}[/tex]
[tex]V_{A} + V_{D}[/tex]
[tex]V_{D} [/tex]

Homework Equations



Kirchhoff's voltage rule for closed circuit loops

The Attempt at a Solution



So I know Kirchhoff's voltage rule for closed circuit loops states that the voltage in a closed circuit is 0.

I think that the answer would be[tex]V_{A} + V_{B} + V_{C} + V_{D}[/tex].

am I right?
 
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  • #2
Think about what you're looking for, you want to know the voltage of the battery. If the battery were, say, 5 V, that means you could say the top part of that circuit, all the lines immediately connected to the + terminal of the battery, were at 5 volts, whereas all the lines immediately connected to the negative terminal were at ground

Also I'll tell you I think there are two answers, however I think only one is present as a choice, and it's not the one you picked
 
  • #3
blochwave said:
Think about what you're looking for, you want to know the voltage of the battery. If the battery were, say, 5 V, that means you could say the top part of that circuit, all the lines immediately connected to the + terminal of the battery, were at 5 volts, whereas all the lines immediately connected to the negative terminal were at ground

Also I'll tell you I think there are two answers, however I think only one is present as a choice, and it's not the one you picked

Well, according to Kirchhoff's voltage rule for closed circuit loops, V_B and V_C should be 0, so if that's true then it should be V_A+V_D since the voltage has been split into the two paths
 
  • #4
Voltage doesn't split like that. If Vb and Vc were not there, then the voltage drop across Va and Vd would be the same(that'd driven by the voltage source), and your answer

By saying that Vb and Vc = 0, well, you're basically saying they're just more wire, not resistors, and that Va is hooked to the plus terminal of the battery, as is Vd, and both other ends connect directly to the negative terminal, and your answer would be either Va or Vd
 
  • #5
Lets start over here. You said you know that Kirchoff's voltage law (KVL) states that the sum of all voltages in a closed loop is equal to zero. Simply apply this law to one of the closed loops in your circuit. In the circuit you have drawn above there are 3 loops that go to ground, 2 of these 3 loops can directly provide you with the voltage you seek namely the voltage across the battery, let's call it V_bat.

I will apply KVL to one of the 3 loops as an example in a clockwise direction:

-V_bat+V_A+V_B=0

rearranging terms...

V_bat=V_A+V_B

I hope this helps you, there is also another solution to this problem that I will leave for you to figure out. The same priciples apply.
 
  • #6
Yes, got the answer. Thank you both.
 
  • #7
I don't understand this, I thought A,B,C, & D summed together would equal the voltage in the battery because there are parallel components in the figure, so the voltage splits unequally between A and D and splits equally between B & C.
 
  • #8
MitsuShai said:
I don't understand this, I thought A,B,C, & D summed together would equal the voltage in the battery because there are parallel components in the figure, so the voltage splits unequally between A and D and splits equally between B & C.

A loop is a single, closed, non bifurcating, non self-crossing path through the circuit. Can you show us how you would draw the loop A,B,C,D?

A corollary of the loop law is that if you pick any two distinct points (call them 1 and 2) along the path of the loop (that is, they are not the same node), then the loop is divided into two distinct paths from one point to the other, and the sum of the voltages for both paths from point 1 to point 2 must be equal.

In the case of this circuit, if you pick the two points to be at the two battery leads, then there are precisely three paths through the circuit that can form the "other path" of the closed loop. You should be able to identify them.
 
  • #9
gneill said:
A loop is a single, closed, non bifurcating, non self-crossing path through the circuit. Can you show us how you would draw the loop A,B,C,D?

A corollary of the loop law is that if you pick any two distinct points (call them 1 and 2) along the path of the loop (that is, they are not the same node), then the loop is divided into two distinct paths from one point to the other, and the sum of the voltages for both paths from point 1 to point 2 must be equal.

In the case of this circuit, if you pick the two points to be at the two battery leads, then there are precisely three paths through the circuit that can form the "other path" of the closed loop. You should be able to identify them.

Ok, I got it now. Thank you :)
 

Related to Kirchhoff's Loop Rule Conceptual Question

1. What is Kirchhoff's Loop Rule Conceptual Question?

Kirchhoff's Loop Rule Conceptual Question is a fundamental concept in the study of electrical circuits. It states that the sum of the potential differences around a closed loop in a circuit is equal to zero.

2. How is Kirchhoff's Loop Rule applied in circuit analysis?

Kirchhoff's Loop Rule is applied in circuit analysis by using it to calculate the unknown currents and voltages in a circuit. By setting up a system of equations based on the loop rule, the values of these unknowns can be determined.

3. Can Kirchhoff's Loop Rule be applied to any type of circuit?

Yes, Kirchhoff's Loop Rule can be applied to any type of circuit, whether it is a series circuit, parallel circuit, or a combination of both. It is a fundamental law that applies to all electrical circuits.

4. What is the significance of Kirchhoff's Loop Rule in circuit analysis?

Kirchhoff's Loop Rule is significant in circuit analysis because it allows us to determine the values of unknown currents and voltages in a circuit. It also helps us to understand the behavior of electrical circuits and how they function.

5. How does Kirchhoff's Loop Rule relate to conservation of energy?

Kirchhoff's Loop Rule is related to the conservation of energy because it is based on the principle of energy conservation. The sum of the potential differences around a closed loop in a circuit must be zero, which means that the energy used in the circuit must be equal to the energy supplied by the source.

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