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# solutions3 - PHYSICS 222 Section 3 EXAM 3 SOLUTIONS 1[18pt...

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PHYSICS 222 Section 3 EXAM 3 SOLUTIONS 1. [18pt] In the figure, E 1 E 2 and Find the currents through each resistor, including the correct sign relative to the arrows shown. Clearly show the equations you derive for this circuit before solving them: obtaining three fully-specified independent equations for the currents is worth 9 points, and solving them is worth another 9 points. Kirchhoff’s Loop Law for the upper loop (clockwise from the vertex at the left of ): E (1) Kirchhoff’s Loop Law for the lower loop (counterclockwise from the vertex at the left of ): E (2) Kirch hoff’s Junction Law for the vertex to the right of (3) One more Kirch hoff’s Loop Law equation is possible. The outer loop gives E E (4) This is the sum of equations (1) and (2), so it is not independent, but it could be substituted for one of them. Substituting into (2) eliminates giving (5) Adding equations (1) and (5) term-by-term eliminates giving Substituting this value of into (1) gives Finally, (3) gives + +

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