Finding the Current in a circuit

In summary, the conversation discusses a circuit problem that involves finding the value of I1. The equations used to solve the problem include Kirchoff's Circuit Law, Kirchoff's Voltage Law, and Ohm's Law. The student has derived two equations using KVL but has encountered sign errors. They are unsure of which sign is incorrect and seek clarification on the matter.
  • #1
John Wiggum
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Homework Statement


The diagram below shows a circuit where; R1 = 5.0 Ω, R2 = 8.0 Ω, R3 = 1.0 Ω, V1 = 16.8 Volts, V2 = 1.5 Volts, and V3 = 39.6 Volts. What is the value of I1? In solving this problem, initially pick the current directions as shown. If the actual current turns out to be in the opposite direction, then your answer will be negative. If you get a negative number, enter it as negative.

Here is a diagram of the circuit with assumed directions of current.\

It should also be noted that my Physics class counts crossing a battery in a KVL loop from its negative terminal to its positive terminal as a positive voltage, and crossing a resistor in a KVL loop in the flow of net positive charge as a negative contribution to voltage for the KVL loop equations.

Homework Equations


[/B]
Kirchoff's Circuit Law: ##Σ I_{in} = Σ I_{out}##

Kirchoff's Voltage Law: ##Σ_{closed~loop} ΔV_i = 0##

Ohm's Law: ##V=I*R##

The Attempt at a Solution


[/B]
So based on the problem picture, and using KCL I determined ##I_1 + I_2 + I_3 = 0## for one of my equations. Then using KVL and drawing two circuit loops shown here I derived two equations. The equation for the 1st loop I found to be ##-I_1*R_1 - V_1 + I_2*R_2 + V_2 = 0##, and I found the equation from the second loop to be ##-I_2*R_2-V_2+I_3*R_3+V_3=0##. When setting up a system of equations and solving them I get ##I_1##=0.5833 amps. This is wrong though and I believe it is a sign error in one of my KVL equations. However, I am unsure of what sign is the issue.
 
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  • #2
Welcome to PF!
John Wiggum said:
So based on the problem picture, and using KCL I determined ##I_1 + I_2 + I_3 = 0## for one of my equations.
This isn't correct. You should be setting up the equation ##Σ I_{in} = Σ I_{out}##. Which junction are you using to set up the equation? For that junction, which currents are "in" and which are "out"? [EDIT: Your equation is correct!]

Then using KVL and drawing two circuit loops shown here I derived two equations. The equation for the 1st loop I found to be ##-I_1*R_1 - V_1 + I_2*R_2 + V_2 = 0##, and I found the equation from the second loop to be ##-I_2*R_2-V_2+I_3*R_3+V_3=0##. When setting up a system of equations and solving them I get ##I_1##=0.5833 amps. This is wrong though and I believe it is a sign error in one of my KVL equations. However, I am unsure of what sign is the issue.
You have some sign errors in both of these equations. Make sure that you start at one point of the loop and go around the loop in one direction (clockwise or counterclockwise) until you return to the starting point. Be sure to follow the sign rules exactly as you stated them below:
It should also be noted that my Physics class counts crossing a battery in a KVL loop from its negative terminal to its positive terminal as a positive voltage, and crossing a resistor in a KVL loop in the flow of net positive charge as a negative contribution to voltage for the KVL loop equations.
 
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  • #3
TSny said:
Welcome to PF!
This isn't correct. You should be setting up the equation ##Σ I_{in} = Σ I_{out}##. Which junction are you using to set up the equation? For that junction, which currents are "in" and which are "out"?

You have some sign errors in both of these equations. Make sure that you start at one point of the loop and go around the loop in one direction (clockwise or counterclockwise) until you return to the starting point. Be sure to follow the sign rules exactly as you stated them below:
Thanks for the quick reply! I guess I should have clarified in my original statement I was using the middle top junction of the circuit diagram to define my KCL equation. As for why I decided that the combination of all three of them is 0 is because in the original problem picture it draws all currents leaving the battery at the positive terminals and I thought all currents would then meet in the middle and equal zero. This would mean that at least one of my three currents is negative meaning the original direction of at least one of the currents is wrong, but I thought the sign conventions would take care of that.
 
  • #4
John Wiggum said:
Thanks for the quick reply! I guess I should have clarified in my original statement I was using the middle top junction of the circuit diagram to define my KCL equation. As for why I decided that the combination of all three of them is 0 is because in the original problem picture it draws all currents leaving the battery at the positive terminals and I thought all currents would then meet in the middle and equal zero. This would mean that at least one of my three currents is negative meaning the original direction of at least one of the currents is wrong, but I thought the sign conventions would take care of that.
OK. Yes, all currents are going into the top junction. So, you are correct here. I was wrong.

I don't understand your handwritten drawings. In loop 1 you have I2 as going down through R2. But the original drawing has it going up. Also, in this loop you have the current along the bottom of the loop labeled as I2, but shouldn't it be I1?

In loop 2, shouldn't the current along the horizontal top part of the loop be I3 toward the left instead of I2 toward the right? Also, shouldn't I3 be upward through R3? And I3 along the bottom of the loop should be toward the right.
 
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TSny said:
OK. Yes, all currents are going into the top junction. So, you are correct here. I was wrong.

I don't understand your handwritten drawings. In loop 1 you have I2 as going down through R2. But the original drawing has it going up. Also, in this loop you have the current along the bottom of the loop labeled as I2, but shouldn't it be I1?

In loop 2, shouldn't the current along the horizontal top part of the loop be I3 toward the left instead of I2 toward the right? Also, shouldn't I3 be upward through R3? And I3 along the bottom of the loop should be toward the right.
Oh good catch! My current is incorrect for loop 2 Thank you! When setting up a KVL loop I was told to pick either a clockwise or counter clockwise direction for the current flow, and as long as I have my signs correct for my KVL equation it should still work out.
 
  • #6
John Wiggum said:
Oh good catch! My current is incorrect for loop 2 Thank you! When setting up a KVL loop I was told to pick either a clockwise or counter clockwise direction for the current flow, and as long as I have my signs correct for my KVL equation it should still work out.
Yes, that's right. Which way did you go around loop 1? Clockwise or counterclockwise? Do you still think your equation for this loop is correct?
 
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TSny said:
Yes, that's right. Which way did you go around loop 1? Clockwise or counterclockwise? Do you still think your equation for this loop is correct?
OK so I went dark on Sunday, but I just wanted to let you know that, Yes I got it! It ended up being a sign error with my two resistors on both my loops. In the end I got my final KVL equations to be ##Loop_1, 0 = -I_1*R_1+V_1+I_2*R_2 - V_2 = 0##, and ##Loop_2, 0 = I_2*R_2 - V_2 - I_3*R_3 + V_3 = 0##.

Thanks for all your help! It turns out that many of the help pages I was looking at on the internet had opposite sign conventions to the ones taught in my class, and I was thus mixing them together to produce wrong equations.
 
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Related to Finding the Current in a circuit

What is current and how is it measured?

Current is the flow of electric charge through a circuit, measured in units of amperes (A). It can be measured using an ammeter, which is connected in series with the circuit, and measures the amount of current passing through a specific point in the circuit.

How do I calculate the current in a circuit?

To calculate the current in a circuit, you can use Ohm's Law, which states that current (I) is equal to the voltage (V) divided by the resistance (R). This can be represented as I = V / R. You can also use Kirchhoff's Current Law, which states that the total current entering a junction in a circuit is equal to the total current leaving the junction.

What factors affect the amount of current in a circuit?

The amount of current in a circuit is affected by the voltage, resistance, and the type of material the circuit is made of. Higher voltage and lower resistance will result in a larger current, while lower voltage and higher resistance will result in a smaller current. The type of material used in the circuit can also affect the flow of current, as different materials have different levels of conductivity.

What is the difference between direct current (DC) and alternating current (AC)?

Direct current is a type of electrical current where the flow of charge is in one direction, while alternating current is a type of electrical current where the flow of charge changes direction periodically. DC is commonly used in batteries and electronic devices, while AC is used in household electricity.

How does the presence of a resistor affect the current in a circuit?

A resistor is a component in a circuit that resists the flow of electric current. When a resistor is present in a circuit, it will decrease the amount of current flowing through the circuit, as it creates a barrier to the flow of charge. The amount of resistance in a circuit can be adjusted to control the amount of current flowing through it.

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