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Unformatted text preview: Solution for Homework 12 Kirchhoffs Laws Solution to Homework Problem 12.1(Voltage Across Parallel Resistor) Problem: In the resistance network to the right all resistors are 2 and the battery is 6V . Calculate the current through R 3 . Select One of the Following: (a) 6 / 5A (b-Answer) 3 / 5A (c) 5 / 6A (d) 5 / 12A (e) 5 / 3A R 1 R 3 R 2 R 4 Solution The equivalent resistance of the parallel circuit is 1 R p = 1 R 2 + 1 R 3 or R p = 1 . The equivalent circuit with the parallel resistor reduced is drawn to the right. The equivalent resistance of the full circuit is then R eq = R 1 + R + p + R 4 = 5 . The current drawn by the circuit is then I = V/R eq = 6 5 A . The potential difference across R p is then V p = IR p = 6 5 V . This is the same potential difference that exists across R 3 . Since V 3 = 6 / 5V and R 3 = 2 , by Ohms Law I 3 = V 3 /R 3 == 6 / 5V / 2 = 3 / 5A R 1 R 3 R 2 R 4 Total Points for Problem: 3 Points Solution to Homework Problem 12.2(Intensities of Bulbs in a Series Circuit When Another Bulb is Added) Problem: Several lightbulbs are connected in series. What happens to the brightnesses of the bulbs when an additional bulb is connected in series with the rest? Select One of the Following: (a) The bulbs get brighter. 1 (b) The bulbs stay the same brightness. (c-Answer) The bulbs get dimmer. (d) It depends on the properties of the bulb added, so it cant be determined from the information given. (e) None of the above. Solution When another bulb is incorporated into the circuit, the resistance of the entire circuit increases. This results in less current in the entire circuit and in the lamps in the circuit. Less current through the bulbs means that the bulbs will dim. Total Points for Problem: 3 Points Solution to Homework Problem 12.3(Connecting Resistors So That Total Resistance is Less Than the Resistance of Any Resistor in the Circuit ) Problem: Should two resistors in a circuit be connected in series or in parallel if the total resistance of the circuit needs to be smaller than the resistance of either of the two resistors?...
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