Simple Circuit with Resistors and Two Batteries

In summary, the circuit in the figure is composed of two batters (E1 = 5 V and E2 = 9 V) and four resistors (R1 = 110 W, R2 = 40 W, R3 = 50 W, and R4 = 50 W) as shown.Find I1 and I3
  • #1
hydr
7
0

Homework Statement



showmepl.gif


The circuit in the figure is composed of two batters (E1 = 5 V and E2 = 9 V) and four resistors (R1 = 110 W, R2 = 40 W, R3 = 50 W, and R4 = 50 W) as shown.

Find I1 and I3

Homework Equations



Well we need to apply KCL. I know the respective voltages (Ohm's law) need to add up to 0.

The Attempt at a Solution



I have tried like a million different equations for the 2 circuits present. I don't really understand circuits too well (which explains as to why I am posting/getting the wrong answer).

For the left loop:

I1R1 - I2R2 + E2 + I3R4 - E1 = 0 (Is it right to assume that I4 has equal current to I3?)

For the left loop:

I2R2 + I3R3 - E2 = 0

I1 + I2 = I3

To see the work that I did on the image to get the directions of the currents go to: http://i30.photobucket.com/albums/c309/hydr/showmepl-1.gif

I know the above equations are wrong, but I don't know what's wrong with them. They look right to me.

I solved for I1 first, but got the wrong answer. I know that if i add the left and right loop together then I should get the equation for the whole loop minus I2R2 and E2. I don't understand what I am doing wrong. I have inputed the respective values into a 3 x 3 matrix and solved for I1-3 with matlab, so there is no error in substitution.
 
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  • #2
hydr said:
I1R1 - I2R2 + E2 + I3R4 - E1 = 0 (Is it right to assume that I4 has equal current to I3?
There's your mistake. Where is I4 flowing? Where is I3? Is there any node (circuit junction) in between the points were I3 and I4 are flowing?
 
  • #3
Defennder said:
There's your mistake. Where is I4 flowing? Where is I3? Is there any node (circuit junction) in between the points were I3 and I4 are flowing?

So in other words, you're saying that since there is no potential difference between the negative sides of the batteries (where I4 is) then there is no current? I am sorry, I am really confused with the current flow thing.
 
  • #4
No, I'm not saying that. What is Kirchoff's current law here? How would you apply it to get I4? Do you even need to label the current separately as I4? Is it not already given by the expressions for the other current labels?
 
  • #5
hydr said:
So in other words, you're saying that since there is no potential difference between the negative sides of the batteries (where I4 is) then there is no current? I am sorry, I am really confused with the current flow thing.

Whoa. Wait a minute here. I4 must equal I1. Current in = current out of the battery.

You have to solve for I1 and I3.

I3 is only part of the loop equation for the 5V battery side as it affects R2
 
  • #6
LowlyPion said:
Whoa. Wait a minute here. I4 must equal I1. Current in = current out of the battery.

You have to solve for I1 and I3.

I3 is only part of the loop equation for the 5V battery side as it affects R2

Ok. Looking at the KCL, I understand, now, how I1 = I4. I also mislabeled my I2 current, it appears it should be facing south instead of north. Using this information and correcting my mistake relating the currents. I now have:

I1R1 + I2R2 + E2 + I1R4 - E1 = 0

-I2R2 + I3R3 - E2 = 0

I2 + I3 = I1

Am I correct to think that the I2 was initially incorrect?
 
  • #7
It doesn't matter which direction you label your I2 current. It'll all work out negative if it's in the wrong direction. Your current equations appear correct, but your only mistake has got to do with I4 and nothing else.
 
  • #8
Defennder said:
It doesn't matter which direction you label your I2 current. It'll all work out negative if it's in the wrong direction. Your current equations appear correct, but your only mistake has got to do with I4 and nothing else.

Ok thanks a bunch. I am pretty sure I understand this now.
 

FAQ: Simple Circuit with Resistors and Two Batteries

What is a simple circuit?

A simple circuit is a closed loop of electrically conductive material that allows electric current to flow through it. It typically consists of a power source, such as a battery, wires, and one or more components, such as resistors, that control the flow of electricity.

What is the purpose of resistors in a circuit?

Resistors are used in circuits to control the flow of electric current. They are designed to resist the flow of electricity and reduce the amount of current that passes through a circuit. This is important in preventing damage to the other components in the circuit, as well as controlling the amount of voltage and current that reaches the different parts of the circuit.

How do resistors affect the brightness of a light bulb in a circuit?

Resistors can be used to control the amount of current that reaches a light bulb in a circuit. By increasing the resistance of the resistor, the amount of current passing through the circuit is reduced, resulting in a dimmer light bulb. Similarly, decreasing the resistance will increase the current flow, making the light bulb brighter.

What happens if the resistors in a circuit are connected in series?

When resistors are connected in series, the total resistance in the circuit increases. This means that the current flowing through the circuit will be reduced, resulting in a decrease in the brightness of the light bulb. Additionally, the voltage across each resistor will be divided proportionally based on their individual resistances.

What happens if the resistors in a circuit are connected in parallel?

When resistors are connected in parallel, the total resistance in the circuit decreases. This results in an increase in current flow, making the light bulb brighter. The voltage across each resistor will be the same, but the total current will be divided among the resistors based on their individual resistances. In this configuration, the resistors act as separate paths for the current to flow through.

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