In the above circuit: V1 = 9.00 V V2 = 12.00 V V3 = 6.00 V R1 = 110.0 R3 = 80.0

Question

In the above circuit: V1 = 9.00 V V2 = 12.00 V V3 = 6.00 V R1 = 110.0 R3 = 80.0 Because of the direction of the batteries, a student looking at the above circuit makes this guess for the direction of current across resistors R1 and R3.

Is the student right, or wrong?

Find the current across resistors R1 and R3.

If the student's choice of direction is RIGHT, the sign of the respective current you enter should be POSITIVE. If the student's choice of direction is WRONG, the sign of that current should be NEGATIVE. (Don't discount the possibility that a current might be zero, either!) (If you have trouble, this hint: Note that the central battery polarity is OPPOSITE what you would expect to make a nice, neat loop. How do you think you should handle two batteries in a loop that are hooked up with OPPOSITE, not the same, polarities?)

I1 = A

I3 = A

Explanation / Answer

v1 - I1 R1 - v2 = 0 , v3 - I3 R3 - v2 = 0

9 - x * 110 - 12 = 0 , 6 - y * 80 - 12 = 0

I1 = -0.0273 A

I3 = -0.075 A

The student is not right. Both directions of currents must be revised.

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