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Unformatted text preview: Homework 8 Solutions Spring 2010 Required Problems Chapter 26 24. Find the maximum current and resulting voltage for each resistor under the power restriction. ( 29 ( 29 2 2 3 1800 1800 3 , 0.5W 0.0167A 0.5W 1.8 10 30.0V 1.8 10 V P P I R I V RP R R I V = = → = = = = = × Ω = × Ω ( 29 ( 29 ( 29 ( 29 3 2800 2800 3 3 3700 3700 3 0.5W 0.0134A 0.5W 2.8 10 37.4V 2.8 10 0.5W 0.0116A 0.5W 3.7 10 43.0V 3.7 10 I V I V = = = × Ω = × Ω = = = × Ω = × Ω The parallel resistors have to have the same voltage, and so the voltage across that combination is limited to 37.4 V. That would require a current given by Ohm’s law and the parallel combination of the two resistors. ( 29 parallel parallel parallel parallel 2800 2100 1 1 1 1 37.4V 0.0235A 2800 3700 V I V R R R = = + = + = Ω Ω This is more than the maximum current that can be in 1800 R . Thus the maximum current that 1800 R can carry, 0.0167A , is the maximum current for the circuit. The maximum voltage that can be applied across the combination is the maximum current times the equivalent resistance. The equivalent resistance is the parallel combination of 2800 R and 3700 R added to 1800 R . ( 29 1 1 max max eq max 1800 2800 3700 1 1 1 1 0.0167A 1800 2800 3700 56.68V 57V V I R I R R R-- = = + + = Ω + + Ω Ω = ≈ 25. ( a ) Note that adding resistors in series always results in a larger resistance, and adding resistors in parallel always results in a smaller resistance. Closing the switch adds another resistor in parallel with R 3 and R 4 , which lowers the net resistance of the parallel portion of the circuit, and thus lowers the equivalent resistance of the circuit. That means that more current will be delivered by the battery. Since R 1 is in series with the battery, its voltage will increase. Because of that increase, the voltage across R 3 and R 4 must decrease so that the total voltage drops around the loop are equal to the battery voltage. Since there was no voltage across R 2 until the switch was closed, its voltage will increase. To summarize: V 1 and V 2 increase ; V 3 and V 4 decrease ( b ) By Ohm’s law, the current is proportional to the voltage for a fixed resistance. Thus I 1 and I 2 increase ; I 3 and I 4 decrease ( c ) Since the battery voltage does not change and the current delivered by the battery increases, the power delivered by the battery, found by multiplying the voltage of the battery by the current delivered, increases . ( d ) Before the switch is closed, the equivalent resistance is R 3 and R 4 in parallel, combined with R 1 in series....
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- Spring '08
- Resistor, Electrical resistance, equivalent resistance