Confused as to where I begin to solve this circuit branch problem

In summary, the conversation discusses simplifying a resistor circuit by finding an equivalent resistance and applying Kirchhoff's Laws. It is suggested to use the fact that current splits at a junction in proportion to the conductivities to simplify the circuit and calculate voltage dividers. The conversation also mentions using the voltmeter to find the overall voltage and explains how this can be extended to multiple branches.
  • #1
naftacher
7
1
Homework Statement
When the ammeter reads 7 A, the voltmeter reads
Relevant Equations
I would assume this requires simple V=iR (ohms) and likely Kirchoff's Laws surrounding currents.
Screenshot 2020-07-01 at 14.27.15.png

I am thinking that this circuit needs to be simplified somehow? Finding an equivalent resistance and moving from there?
 
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  • #2
One can try simplification.
But if that doesn't work, one could try applying Kirchhoff's Laws
 
  • #3
naftacher said:
Homework Statement:: When the ammeter reads 7 A, the voltmeter reads
Relevant Equations:: I would assume this requires simple V=iR (ohms) and likely Kirchoff's Laws surrounding currents.

View attachment 265636
I am thinking that this circuit needs to be simplified somehow? Finding an equivalent resistance and moving from there?
What is the impedance of an ideal voltmeter? So how much current gets diverted through it? Use that fact to simplify the resistor circuit to find the overall voltage, then break it back into the two branches to calculate the voltage dividers, etc. :smile:
 
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  • #4
At a junction like the one in your diagram, current will split in proportion to the conductivities, so ##i_A = \frac{R_B}{R_A + R_B}i##
$$i_A R_A = i_B R_B \implies i_B = \frac{R_A}{R_B} i_A$$and as such we have$$i = i_A + i_B = i_A \left (1 + \frac{R_A}{R_B} \right) = i_A \left(\frac{R_A + R_B}{R_B} \right)$$so the current flowing down the branch with resistance ##R_A## is$$i_A = \frac{R_B}{R_A + R_B}i$$
 
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  • #5
etotheipi said:
At a junction like the one in your diagram, current will split in proportion to the conductivities, so ##i_1 = \frac{R_2}{R_1 + R_2}i##
$$i_1 R_1 = i_2 R_2 \implies i_2 = \frac{R_1}{R_2} i_1$$and as such we have$$i = i_1 + i_2 = i_1 \left (1 + \frac{R_1}{R_2} \right) = i_1 \left(\frac{R_1 + R_2}{R_2} \right)$$so the current flowing down the branch with resistance ##R_1## is$$i_1 = \frac{R_2}{R_1 + R_2}i$$
I have seen this equation before. How am I to extend this to R3 and R4? or do I not need to
 
  • #6
naftacher said:
I have seen this equation before. How am I to extend this to R3 and R4? or do I not need to

Whoops, don't take the numbers too literally, I've changed them to A's and B's to make it more general. It's applying to cases where you have multiple branches of different resistance between two nodes. ##R_A## and ##R_B## are the total resistances of those branches.

@berkeman gave you an important hint about the voltmeter, to explain why we can use the reasoning we did to get that result...
 
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1. How do I identify the different components in the circuit branch problem?

To begin solving a circuit branch problem, you will need to identify all the components in the circuit, including resistors, capacitors, and voltage sources. These components can be identified by their symbols and values, which are typically labeled on the circuit diagram.

2. What is the purpose of solving a circuit branch problem?

The purpose of solving a circuit branch problem is to determine the current and voltage at different points in the circuit. This information can be used to analyze the behavior of the circuit and make any necessary adjustments or repairs.

3. How do I use Kirchhoff's Laws to solve the circuit branch problem?

Kirchhoff's Laws are used to analyze the flow of current and voltage in a circuit. The first law, also known as the Law of Conservation of Charge, states that the total current entering a junction must equal the total current leaving the junction. The second law, also known as the Law of Conservation of Energy, states that the sum of the voltage drops in a closed loop must equal the sum of the voltage sources in that loop.

4. What are some common strategies for solving a circuit branch problem?

Some common strategies for solving a circuit branch problem include using Ohm's Law to calculate voltage, current, and resistance, using series and parallel circuit rules to simplify the circuit, and using nodal analysis or mesh analysis to solve for unknown values.

5. What should I do if I am still confused about solving the circuit branch problem?

If you are still confused about solving the circuit branch problem, it can be helpful to break the problem down into smaller parts and solve each part individually. You can also seek help from a teacher, tutor, or fellow student who is knowledgeable in circuit analysis. Practice and repetition can also improve your understanding and ability to solve these types of problems.

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