Understanding Total Voltage in Parallel Circuits

In summary, the conversation discusses the relationship between total voltage and voltage drop over different resistors in a circuit, as well as the application of voltage and the use of Kirchoff's law. It is explained that the voltage drop is independent of the path chosen and is a property of a conservative field, and that the potential at different nodes can be calculated to determine currents. The conversation also emphasizes the importance of visualizing the circuit with a power source to better understand the concept.
  • #1
physics_CD
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Homework Statement
I have this resistor which is connected to some battery (not very important). I don't understand why the total voltage is equal to the voltage drop over the 3 Ω and 2 Ω resistors. Why is it not dependent on the resistor in the middle with 4 Ω . I do understand it if the 4 Ω were substituted with a wire. But how can it be that there is no difference whether it is 4 Ω or 0 Ω?
Relevant Equations
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I really don't have any clue why the total voltage is equal to the voltage drop over the 3 Ω and 2 Ω resistors and independent of the 4 Ω resistor . Does it have to do with parallel circuits?
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  • #2
And just where are you applying the voltage. Your circuit is incomplete without showing that. I assume it's on the far left and far right but you need to say. Draw the circuit WITH the power source.
 
  • #3
phinds said:
And just where are you applying the voltage. Your circuit is incomplete without showing that. I assume it's on the far left and far right but you need to say. Draw the circuit WITH the power source.

Yes it is the far left and far right. I am sorry for not mentioning it.
 
  • #4
There are a few ways of thinking about it. Suppose the potential on the far left is A volts, the potential at the node between the ##2\Omega## and ##3\Omega## resistors is B volts, and the potential on the far right is C Volts. Then the magnitude of the change in potential tracing along the very top loop is the sum of the individual changes: ##(A-B) + (B-C) = A-C##.

This is similar to how Kirchoff's law is formulated, though we would need to have a closed loop like @phinds mentioned to apply it, with the power source connected to the far left and far right.
 
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  • #5
etotheipi said:
There are a few ways of thinking about it. Suppose the potential on the far left is A volts, the potential at the node between the ##2\Omega## and ##3\Omega## resistors is B volts, and the potential on the far right is C Volts. Then the magnitude of the change in potential tracing along the very top loop is the sum of the individual changes: ##(A-B) + (B-C) = A-C##.

This is similar to how Kirchoff's law is formulated, though we would need to have a closed loop like @phinds mentioned to apply it, with the power source connected to the far left and far right.
But there are different ways I can go from A to B. Does this mean that the voltage drop is independent of which path I choose to go? (I assume that I can't go over the same path)
 
  • #6
physics_CD said:
But there are different ways I can go from A to B. Does this mean that the voltage drop is independent of which path I choose to go? (I assume that I can't go over the same path)

Yes. The magnitude of the potential difference between the two end points is ##A-C##, since that is what we've labeled them. Now if we trace along any possible path from one end to the other, and add up all of the changes in potential as we go, we'll always end up with this value. It is a property of a conservative field that the change in potential energy is only dependent on the start and end points.

Of course, if want to start figuring out the currents through individual components, we will need to work out the potentials at some of the nodes in the middle.
 
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  • #7
@physics_CD you are seriously overthinking this. If you have a battery hooked to the far left and far right, WHY would you expect the voltage of the battery to be effected by the value of the resistors (unless they were ALL zero in which case you'd have a short circuit)?

IF you would just DRAW the battery the way I asked I think it might be more clear to you.
 
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FAQ: Understanding Total Voltage in Parallel Circuits

1. What is voltage?

Voltage is a measure of the electric potential difference between two points in an electric circuit. It is commonly represented by the letter V and is measured in volts (V).

2. How is voltage different from current?

Voltage and current are two different properties of electricity. While voltage is the measure of electric potential difference, current is the measure of the flow of electric charge. Voltage can be thought of as the force that pushes the electric charge through a circuit, while current is the amount of charge that actually flows.

3. What is the unit of measurement for voltage?

The unit of measurement for voltage is the volt (V). One volt is defined as the amount of electric potential required to cause a current of one ampere (A) to flow through a resistance of one ohm (Ω).

4. How is total voltage calculated in a circuit?

In a series circuit, the total voltage is the sum of the individual voltage drops across each component. In a parallel circuit, the total voltage is equal to the voltage across each branch. The total voltage can also be calculated using Ohm's law, which states that voltage is equal to the product of current and resistance (V = I x R).

5. What factors can affect the total voltage in a circuit?

The total voltage in a circuit can be affected by various factors, including the number and arrangement of components, the material and length of the conductors, and the presence of any external sources of electricity. Changes in any of these factors can result in a change in the total voltage of a circuit.

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