I was checking my notebook section on Kirchhoff's law. It's been a long time since I've used it, I wanted to review. For an example, I found this circuit:
A basic circuit. Component values:
Voltage source (Vs) = 9V
R1 = 100 ohms
R2 = 2.2k
R3 = 10k
I'm solving for current I1.
With simulation software, I know that the current going through the battery should be around 4.7mA. I get the same answer when simplifying the circuit V/(R2||R3 + R1). But here comes the issue.
Using Kirchhoff's laws, I get three equations:
I1 - I2 - I3 = 0
R1*I1 - R2*I2 = Vs
R2*I2 - R3*I3 = 0
Apparently these equations are wrong! I am totally baffled as to why, I've been hitting my against a while trying to find the error in them. Because when I solve for those equations, I get I1 = 3mA, I2 = 4mA, and I3 = 1.7mA. Or more exactly, I1 = 3.08mA, I2 = 3.95mA, I3 = -1.73mA.
You can check that math by solving for a matrix:
1 -1 -1 0
100 -2200 0 9
0 2200 -10000 0
You'll get the same answers. So the issue is in the equations. But where?? I've been over this a million times. Two loops. In loop 1, Vs is polarized positive, Vr1 is negative, Vr2 is negative. In loop 2, Vr2 is positive (assuming clockwise current) and Vr3 is negative. Where am I going wrong? What am I missing? Help is needed. Thanks.
A basic circuit. Component values:
Voltage source (Vs) = 9V
R1 = 100 ohms
R2 = 2.2k
R3 = 10k
I'm solving for current I1.
With simulation software, I know that the current going through the battery should be around 4.7mA. I get the same answer when simplifying the circuit V/(R2||R3 + R1). But here comes the issue.
Using Kirchhoff's laws, I get three equations:
I1 - I2 - I3 = 0
R1*I1 - R2*I2 = Vs
R2*I2 - R3*I3 = 0
Apparently these equations are wrong! I am totally baffled as to why, I've been hitting my against a while trying to find the error in them. Because when I solve for those equations, I get I1 = 3mA, I2 = 4mA, and I3 = 1.7mA. Or more exactly, I1 = 3.08mA, I2 = 3.95mA, I3 = -1.73mA.
You can check that math by solving for a matrix:
1 -1 -1 0
100 -2200 0 9
0 2200 -10000 0
You'll get the same answers. So the issue is in the equations. But where?? I've been over this a million times. Two loops. In loop 1, Vs is polarized positive, Vr1 is negative, Vr2 is negative. In loop 2, Vr2 is positive (assuming clockwise current) and Vr3 is negative. Where am I going wrong? What am I missing? Help is needed. Thanks.