Using Kirchhoff’s rules, (a) find the current in each
resistor shown in Figure P28.31 and (b) find the potential
difference between points c and f.
Σ ΔV = 0 (KVL)
The Attempt at a Solution
I have been trying to set up a system of equations for the three loops as shown in the picture, but I can't seem to get the right numbers. I was able to get the currents using mesh-current analysis; they are 0.38 mA, 3.08 mA, and 2.69 mA for resistors 1, 2 and 3, respectively. However, I would like to know what mistake I'm making in applying basic KVL to the loops. The equations I get for each loop are:
L1: 70V - 60V - V2 - V1 = 0
L2: 60V - V3 - 80V + V2 = 0
L3: 70V - V3 - 80V - V1 = 0
where V1, V2, and V3 correspond to the voltages at R1, R2, and R3, respectively.
One issue I have noted but am unsure of is whether or not V2 in the second equation should be positive or negative. If I assume the current is flowing downward across R2 it is negative in equation 1. Therefore, I should continue to assume current is flowing downward across R2, which would mean V2 is positive for equation 2. Is that correct?
Any help would be greatly appreciated!
I see now that my equations are not providing enough information to solve for the variables. If I solve for V3 in equation 3 and plug that into equation 2, my equation 2 is just the same equation 1. I'm not sure where to go from this point...
I found my problem. I was missing an equation, I1 = I2 + I3. Using this to solve the system of equation yields the correct results.
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