How Does Kirchhoff's Loop Rule Apply to Multi-Battery, Multi-Loop Circuits?

[r_swayze]

(a) What is the magnitude of the current that flows through branch AB? (b) In what direction does the conventional current flow in branch AB? (c) What is the magnitude of the current that flows through branch CD? (d) In what direction does the conventional current flow in branch CD?

I don't know where to start with this problem since there are 3 batteries in two different loops.

I think in the first loop the circuit would be 1.5 A, since 10V + 5V = 15V, and 15V/10ohm = 1.5 A?

And then, for the second loop 4V - I*7ohm - I*10ohm = 0. That circuit would be 0.235 A.

magnitude of the branch AB would be 1.5A + 0.235A = 1.735A

Am I doing this correctly?

and for part d) why is the magnitude of the current flowing to the right? shouldn't it be flowing left since the positive terminal of the battery is on the left side of the negative terminal?

 

[Delphi51]

Your instincts look good, but this really is a network problem and I think you must use the network rules formally. The immediate problem with your solution is that the two loops and their currents are not independent.

Mark I1 on the top branch and give it a direction - I chose left. Mark I2 on the bottom branch and say it goes left, too. Then the current in the center branch is I1 + I2 to the right. Now you can write Kirchoff's rule for the upper loop and again for the lower loop. You'll have a system of two equations with the two unknowns I1 and I2.