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Soln7 - DC Circuits

# Soln7 - DC Circuits - 8B Worksheet Answers 7 DC Circuits 1...

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8B Worksheet Answers 7. DC Circuits 1. Series Circuit a) b) I batt = I 1 = I 2 c) V batt = V 1 + V 2 d) P batt = P 1 + P 2 e) P batt = I batt V batt = I batt V 1 + I batt V 2 = I 1 V 1 = I 2 V 2 = I 1 2 R 1 + I 2 2 R 2 = P 1 + P 2 R eff = 18 Ω I batt = 5 / 9 A P 1 = I 1 2 R 1 = 50 / 27 W P 2 = I 2 2 R 2 = 100 / 27 W P 1 + P 2 = 50 / 9 W P batt = I batt V batt = 50 / 9 W = 5.556 W Parallel Circuit a) b) I batt = I 1 + I 2 c) V batt = V 1 = V 2 d) P batt = P 1 + P 2 e) P batt = I batt V batt = I 1 V batt + I 2 V batt = I 1 V 1 = I 2 V 2 = I 1 2 R 1 + I 2 2 R 2 = P 1 + P 2 R eff = 4 Ω I batt = 5 / 2 A P 1 = V 1 2 / R 1 = 50 / 3 W P 2 = V 2 2 / R 2 = 25 / 3 W P 1 + P 2 = 25 W P batt = I batt V batt = 25 W

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2. Left Circuit a) R eq = 2 R I batt = V batt / 2 R b) Junction Rules: I 1 = I 2 + I 3 A Loop Rules: V batt - I 2 (4 R ) = 0 a - I 3 R - I 3 (2 R ) - I 3 R + I 2 (4 R ) = 0 b Solving Equation b gives I 2 = I 3 b Plugging b ’ into A gives I 1 = 2 I 2 A Solving a gives I 2 = V batt / 4 R a Plugging a ’ into A ’, finally, gives I 1 = V batt / 2 R , (which is what we found in part (a)), so I 1 = V batt / 2 R I 2 = V batt / 4 R I 3 = V batt / 4 R Right Circuit a) R eq = 15 R / 8 I batt = 8 V batt / 15 R b) Junction Rules: I 1 = I 2 + I 3 A Loop Rules: V batt - I 2 (4 R ) - I 2 R = 0 a - I 3 R - I 3 (2 R ) + I 2 R + I 2 (4 R ) = 0 b Solving Equation b gives I 3 = 5/3 I 2 b Plugging b ’ into A gives I 1 = 8/3 I 2 A Solving a gives I 2 = V batt / 5 R a Plugging a ’ into A ’, finally, gives I 1 = 8 V batt / 15 R , (which is what we found in part (a)), so I 1 = 8 V batt / 15 R I 2 = V batt / 5 R I 3 = V batt / 3 R
3. a) 12 bulbs b) 8 bulbs c) The parallel arrangement will result in the lowest effective resistance, and so the highest current. The power delivered by the battery is IV , so a higher current will result in a greater power, which will drain the battery’s energy fastest.

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