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Unformatted text preview: Physics 21 Fall, 2004 Solution, Practice Exam #1 Problem 1. 3 Ω 2 Ω 4 Ω 13 V 4 V 8 V I 1 I 3 I 2 a b 1 2 (a) Write the loop and node equations needed to determine the currents I 1 , I 2 , and I 3 in the circuit shown. node: I 1 = I 2 + I 3 loop 1: 13 − 3 I 1 − 4 I 2 − 8 = 0 loop 2: 8 + 4 I 2 − 2 I 3 + 4 = 0 (b) Determine the currents by explicit solution of the equa tions. Rearrange loop 1 and loop 2 equations: loop 1: 3 I 1 + 4 I 2 = 5 loop 2: 4 I 2 − 2 I 3 = − 12 Use the node equation to eliminate I 3 from the loop 2 equation; multiply the resulting equation by 1.5: 3 I 1 + 4 I 2 = 5 − 3 I 1 + 9 I 2 = − 18 Add to eliminate I 1 , solve to get I 2 . Substitute back to get I 1 then I 3 . Results are I 1 = 3 . 0 A , I 2 = − 1 . 0 A , I 3 = 4 . 0 A (c) Determine the value of the potential difference between point a and point b ( V b − V a ) in the above circuit along the path through the 4 V battery and the 2 Ω resistor. V b = V a − 4 + 2 I 3 = V a − 4 + 8 ⇒ V b − V a = 4 V Problem 2. A line charge density of λ = 6 . × 10 − 7 C/m extends along the yaxis from y = 2 . 0 m to y = 4 . 0 m, as shown....
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 Fall '07
 Hickman
 Physics, Charge, Electric charge, 0.1 m, 0.10 M

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