Which one of the following is a valid Kirchhoff voltage equation for the dotted

Question

Which one of the following is a valid Kirchhoff voltage equation for the dotted outside loop?

Which one of the following is a valid Kirchhoff voltage equation for the dotted outside loop?
-E1 + I1R1 + E4 - I4R4 = 0

-E1 + I1R1 - E4 + I4R4 = 0

-E1 + I1R1 - E4 - I4R4 = 0

Which one of the following is a valid Kirchhoff current equation for the above circuit?
I1 + I2 + I3 + I4 = 0

I1 - I2 + I3 + I4 = 0

I1 + I2 - I3 - I4 = 0

Let E1 = 10 V, E2 = 15 V, R1 = 10 W, and R2 = 20 W. What is the magnitude of the potential difference between points A and B?

Explanation / Answer

a.

We see that (3) is equal to the second choice -?1 + I1R1 - ?4 + I4R4 = 0

b.

We see that (6) is equal to the second choice I1 - I2 + I3 + I4 = 0

Kirchoff's Circuit Laws state that in a closed loop, the potential V is zero. Also, the sum of the current through all junctions is equal to the current before the junction.

There are 5 loops:

?1 - I1R1 - I2R2 - ?2 = 0 (1)

?1 - I1R1 - ?3 + I3R3 = 0 (2)

?1 - I1R1 + ?4 + I4R4 = 0 (3)

-I3R3 + ?3 -I2R2 - ?2 = 0 (4)

-I3R3 + ?3 + ?4 + I4R4 = 0 (5)

Also,

I1 = I2 - I3 - I4 (6)

Above is much more information than we need to solve the questions asked of you.

c.

using (1), we see that

?1 - VAB - ?2 = 0

==> |VAB| = |?1 - ?2| = |10 V - 15 V| = |-5 V| = 5 V

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