Kirchhoff's Rules and Systems of Equations

[succubus]

Homework Statement

To find the current traveling through a circuit with parallel and series connections. The circuit looks something like this.

*Right now my webserver is giving me fits and won't let me login. I will try and get a picture to those who cannot understand what I am about to describe below, and with my poor description skills, will probably be everyone.

It's a series/parallel circuit. First there is R1(97.8), and then the circuit splits into parallel with R3(553) on the outside and R2(325) on the inside, and then continues around to a battery that has a measured voltage of 2.62 volts.

We measured the current in the lab, so we have the answers. The problem is, were supposed to use systems of equations to discover the answer as if we didn't measure it. IO have tried my best to do something about, and these are the equations I have come up with (we were only told to use 3, not the 4th for the inner current) and tried solving for each individual variable to no avail. This is what I've done.

Homework Equations

Outer current
(1) V-R1I1 - R3I3 = 0
Parallel Loop Current (Inside parallel circuit from R3 to R2)
(2) -R3I3 + R2I2 = 0
Junction Rule
(3) I1 = I2 +I3

I'm pretty sure my equations are correct.

I substituted I1 in equation 3 into equation 1 to get

V-R1(I2 + I3) - R3I3 = 0
Then I solved for I2
-R1I2 - R1I3 - R3I3 = -V
-R1I2 - I3(R1 + R3) = -V
-V + I3(R1 + R3) = -R1I2
(Divide by R1)

-V + I3(R3) = - I2

I2 = V - R3I3

Then I substituted what I got for I2 into equation 2

-R3I3 + R2(V-R3I3) = 0

-R3I3 - R2V - R2R3I3 = 0

-R3I3 - R2R3I3 = R2V

-I3(R3 + R2R3) = R2V
Divide by R3 + R2R3 yields

-I3 = V/2R3

which gives me something similar to the current I measured for I3, but 1 decimal off.

Measured currents are below

I1 = 7.43 mA
I2 = 24.3 mA
I3 = 24 mAWhere did I go wrong? When I plug in the answers they don't come anywhere close to what I measured across the circuit. I'm pretty sure we measured the current correctly. :/

 

[SGT]

Homework Statement

To find the current traveling through a circuit with parallel and series connections. The circuit looks something like this.

*Right now my webserver is giving me fits and won't let me login. I will try and get a picture to those who cannot understand what I am about to describe below, and with my poor description skills, will probably be everyone.

It's a series/parallel circuit. First there is R1(97.8), and then the circuit splits into parallel with R3(553) on the outside and R2(325) on the inside, and then continues around to a battery that has a measured voltage of 2.62 volts.

We measured the current in the lab, so we have the answers. The problem is, were supposed to use systems of equations to discover the answer as if we didn't measure it. IO have tried my best to do something about, and these are the equations I have come up with (we were only told to use 3, not the 4th for the inner current) and tried solving for each individual variable to no avail. This is what I've done.

Homework Equations

Outer current
(1) V-R1I1 - R3I3 = 0
Parallel Loop Current (Inside parallel circuit from R3 to R2)
(2) -R3I3 + R2I2 = 0
Junction Rule
(3) I1 = I2 +I3

I'm pretty sure my equations are correct.

I substituted I1 in equation 3 into equation 1 to get

V-R1(I2 + I3) - R3I3 = 0
Then I solved for I2
-R1I2 - R1I3 - R3I3 = -V
-R1I2 - I3(R1 + R3) = -V
-V + I3(R1 + R3) = -R1I2
(Divide by R1)

-V + I3(R3) = - I2

I2 = V - R3I3

Then I substituted what I got for I2 into equation 2

-R3I3 + R2(V-R3I3) = 0

-R3I3 - R2V - R2R3I3 = 0

-R3I3 - R2R3I3 = R2V

-I3(R3 + R2R3) = R2V
Divide by R3 + R2R3 yields

-I3 = V/2R3

which gives me something similar to the current I measured for I3, but 1 decimal off.

Measured currents are below

I1 = 7.43 mA
I2 = 24.3 mA
I3 = 24 mA


Where did I go wrong? When I plug in the answers they don't come anywhere close to what I measured across the circuit. I'm pretty sure we measured the current correctly. :/

You went wrong here:

-V + I3(R1 + R3) = -R1I2
(Divide by R1)

-V + I3(R3) = - I2

R1 + R3 divided by R1 is not R3.

 

[m2003]

It seems like you have the right approach in using Kirchhoff's rules and setting up a system of equations to solve for the current in the circuit. However, there could be a few potential sources of error in your calculations. For example, when you substitute I1 from equation 3 into equation 1, you should get V-R1(I2+I3)-R3I3 = 0 instead of V-R1(I2+I3)-R3I3 = -V. This could be a simple mistake that is throwing off your final answer.

Another potential source of error could be in the measured values for the resistors. Make sure you are using the correct values for R1, R2, and R3 in your calculations. Also, double check your units to make sure they are consistent throughout your equations.

Overall, it seems like you are on the right track and just need to carefully check your calculations and measurements to find the source of the discrepancy. Keep in mind that it is common to have some small differences between calculated and measured values due to experimental error. As long as your calculations are correct and your values are close, your approach should be valid.