(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

What must the emf ε in the figure be in order for the current through the 7.00 ohm resistor to be 1.75A? Each emf source has negligible internal resistance.

2. Relevant equations

Kirchhoff's Rule:

[itex]\sum I=0[/itex] junction rule

[itex]\sum V=0[/itex] loop rule

3. The attempt at a solution

I have drawn my current directions as shown in the attachment below.

By the junction rule, I know that [itex]I_2 = I_3+I_1[/itex] and it is given that [itex]I_2=1.75A[/itex].

I drew a loop clockwise around the entire thing and came up with the following equation:

[itex]24V-(7 ohm)(1.75A)-(I_1)(3 ohm) = 0[/itex]

so that I have

[itex]I_1 = (24V-12.25V)/3= 3.92A[/itex]

and then

[itex]I_3 = I_2 - I_1 = 2.17[/itex]

Drawing loop 2 clockwise within the right inner loop I have the following equation:

[itex]-(7 ohm)(I_2) - (I_3)(2 ohm) + ε = 0[/itex]

solving for ε, I get

[itex]ε = (12.25V)+(4.34V) = 16.59V[/itex]

Also, if I draw a clockwise loop inside the right inner loop, I have the following equation:

[itex]-ε + (I_3)(2 ohm) - (I_1)(3 ohm) + 24 V = 0[/itex]

which simplifies to

[itex]ε = 16.58V[/itex]

I can find no mistakes (and I have checked over my work a few times) but it is the wrong answer. Could anyone please help me? Thanks!

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# Homework Help: Using Kirchhoff's Rules

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