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814_Physics ProblemsTechnical Physics

# 814_Physics ProblemsTechnical Physics - 154 P28.66 Direct...

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154 Direct Current Circuits P28.66 Start at the point when the voltage has just reached 2 3 V and the switch has just closed. The voltage is 2 3 V and is decaying towards 0 V with a time constant R C 2 V t V e C t R C a f = L N M O Q P 2 3 2 . We want to know when V t C a f will reach 1 3 V . Therefore, 1 3 2 3 2 V V e t R C = L N M O Q P or e t R C = 2 1 2 or t R C 1 2 2 = ln . V R 1 R 2 V + C V c Voltage controlled switch FIG. P28.66 After the switch opens, the voltage is 1 3 V , increasing toward V with time constant R R C 1 2 + b g : V t V V e C t R R C a f b g = L N M O Q P + 2 3 1 2 . When V t V C a f = 2 3 2 3 2 3 1 2 V V Ve t R R C = + b g or e t R R C + = 1 2 1 2 b g . So t R R C 2 1 2 2 = + b g ln and T t t R R C = + = + 1 2 1 2 2 2 b g ln . P28.67 (a) First determine the resistance of each light bulb: P = V R a f 2 R V = = = a f a f 2 2 120 60 0 240 P V W . . We obtain the equivalent resistance R eq of the network of light bulbs by identifying series and parallel equivalent resistances:
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