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Quiz03_solutions

# Quiz03_solutions - Name Section QUIZ#3 Physics 222 Fall...

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Name: Section: QUIZ #3 Electric Currents and Resistors Physics 222, Fall 2011 Sep. 13, 2011 Version A Two resistors R and 4 R can be connected in parallel with an ideal battery (no internal resistance) or in series with the same battery. What is the ratio of the total power dissipation in the series circuit to the total power dissipation in the parallel circuit? Solution The power dissipation in the circuit can be calculated by using one of the following three equations: P tot = V 2 R eq , = V I tot , = I 2 tot R eq , where V is the voltage of the battery. Since we are comparing between two situations where the total voltage is the same, the first equation is most suitable for the task. The second and third equations require calculating R eq anyway to get current, so they involve an unnecessary step. We now calculate the total resistance for each of the two connections: Parallel: R parallel = 1 R + 1 4 R - 1 = 4 5 R Series: R series = R + 4 R = 5 R. Then the ratio between the power dissipation in series, P series , and the power dissipation in parallel, P parallel , is: P series P parallel = V 2 /R series V 2 /R parallel = R parallel R series = 4 25 .

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Quiz03_solutions - Name Section QUIZ#3 Physics 222 Fall...

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