- #1

subzero0137

- 91

- 4

**"Use Kirchhoff’s rules to calculate the current through each ideal battery in the figure**

below. R1=1Ω, R2=2Ω, ε1=2V, ε2=ε3=4V. You should apply Kirchoff’s loop rule to the ε1-R1-R2-ε2-R1 loop, and the ε2-R2-R1-ε3-R1 loops respectively, each time starting from the negative end of the battery and assuming that the currents flow in the directions shown."

below. R1=1Ω, R2=2Ω, ε1=2V, ε2=ε3=4V. You should apply Kirchoff’s loop rule to the ε1-R1-R2-ε2-R1 loop, and the ε2-R2-R1-ε3-R1 loops respectively, each time starting from the negative end of the battery and assuming that the currents flow in the directions shown."

**My attempt: i1=i2+i3 (using junction rule).**

Left loop:

ε1-i1R1-i3R2-ε2-i1R1=0, therefore i1+i3=-1A.

Right loop:

ε2+i3R2-i2R1-ε3-i2R1=0, therefore i3=i2.

Therefore i1=-2/3A, i2=-1/3A, and i3=-1/3A. But I'm not sure if these are the final values. The question is asking for currents through each ideal battery, so do I have to change the signs of the i2 and i3?

Left loop:

ε1-i1R1-i3R2-ε2-i1R1=0, therefore i1+i3=-1A.

Right loop:

ε2+i3R2-i2R1-ε3-i2R1=0, therefore i3=i2.

Therefore i1=-2/3A, i2=-1/3A, and i3=-1/3A. But I'm not sure if these are the final values. The question is asking for currents through each ideal battery, so do I have to change the signs of the i2 and i3?