How can I use KVL and KCL to find the potential differences in this circuit?

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In summary, the conversation involves finding the potential differences (in V) in a circuit with a voltage source and three resistors. The equation ε - i1R1 - i2R2 = 0 is derived to find the current through R1 and R2. R3 affects the circuit by creating an asymmetry in the current flow. To find the potential differences, two equations are formed using KVL and KCL, with the unknowns being the currents i1 and i2. Solving the system of equations will give the values of i1 and i2, which can be used to calculate the potential differences.
  • #1
Pochen Liu
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Homework Statement
Finding potential difference across a fancy circuit
Relevant Equations
as attached
In the figure ε = 9.89 V, R1 = 1150 Ω, R2 = 2890 Ω, and R3 = 4940 Ω. What are the potential differences (in V) (a) VA - VB, (b) VB - VC, (c) VC - VD, and (d) VA - VC?What I've tried
I have derived the equation ε - i1R1 - i2R2 = 0

where i1 is the current running through R1 and vice versaQuestions
How does R3 affect the circuit? I am quit confused as it bridges the parallel lines and I'm now not sure how the current runs

Because I want to find out i1 and i2 such that I can then use:

V = IR

to calculate the Voltage on R1 aka point B

and find VA - VB etc
 

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  • #2
Pochen Liu said:
I have derived the equation ε - i1R1 - i2R2 = 0

where i1 is the current running through R1 and vice versa
The current through which R1?
There is a symmetry you can use but you'll have to discover it first.
Pochen Liu said:
How does R3 affect the circuit? I am quit confused as it bridges the parallel lines and I'm now not sure how the current runs
The two sides are not identical. In the left path you have the smaller resistance at the bottom (C will have a lower potential than the average of A and D), in the right path you have the smaller resistance at the top (B will have a higher potential than the average of A and D). There will be a current flow through R3.

You don't need to discover this directly. You can calculate VB-VC assuming that no current flows through R3. If it is non-zero (and it will be) then that assumption is wrong.
 
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you have already made 1 correct equation by applying KVL at the loop ABD+voltage source that contains two unknowns ##I_1,I_2##

Now apply KVL at the loop ACB. The symmetry that @mfb talks about, if you identify it correctly will help you make this equation also with the same unknowns ##I_1, I_2## (and also with the help of applying KCL at node B or node C.

So you ll have two equations with two uknowns, solve the system of equations and you ll know ##I_1,I_2## and everything else can be derived by knowing those 2 values.
 

FAQ: How can I use KVL and KCL to find the potential differences in this circuit?

What is a potential difference?

A potential difference is the difference in electric potential between two points in a circuit. It is measured in volts (V) and is caused by the separation of positive and negative charges.

How do you calculate potential difference?

Potential difference can be calculated by dividing the work done by the charge. The formula is V=W/Q, where V is potential difference, W is work done, and Q is the charge.

What is the unit for potential difference?

The unit for potential difference is volts (V). One volt is equivalent to one joule (J) of energy per coulomb (C) of charge.

How can potential difference be measured?

Potential difference can be measured using a voltmeter, which is a device that measures voltage. It can be connected in parallel to the circuit to measure the difference in potential between two points.

Why is potential difference important in electricity?

Potential difference is important in electricity because it is what drives the flow of electric current. It is also necessary for the functioning of electronic devices and plays a crucial role in various electrical systems.

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