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Physics Assignment

Physics Assignment - Phys 122 TUTORIAL 8 AC Current...

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Phys 122 Introductory Physics II TUTORIAL 8 AC Current. Key 1. According to Equation 20.7, an ac voltage V is given as a function of time t by V = V 0 sin 2 π ft , where V 0 is the peak voltage and f is the frequency (in hertz). For a frequency of 60.0 Hz, what is the smallest value of the time at which the voltage equals one-half of the peak value? SOLUTION From Equation 20.7 we have 1 1 0 0 2 2 sin 2 or sin 2 V V V f t f t π π = = = Using the inverse trigonometric sine function, we find ( 29 1 1 2 2 sin 0.524 f t π - = = In this result, the value of 0.524 is in radians and corresponds to an angle of 30.0º. Thus we find that the smallest value of t is ( 29 3 0.524 0.524 1.39 10 s 2 2 60.0 Hz t f π π - = = = × 2. The average power dissipated in a stereo speaker is 55 W. Assuming that the speaker can be treated as a 4.0- resistance, find the peak value of the ac voltage applied to the speaker. ( 29 2 2 2 0 rms 0 / 2 2 V V V P R R R = = = Solving for the peak voltage V 0 gives ( 29 ( 29 0 2 2 4.0 55 W 21 V V RP = = = 3. A light bulb is connected to a 120.0-V wall socket. The current in the bulb depends on the time t according to the relation I = (0.707 A)sin [(314 Hz) t ]. (a) What is the frequency of the alternating current? (b) Determine the resistance of the bulb’s filament. (c) What is the average power consumed by the light bulb? a. By comparing ( 29 ( 29 0.707 A sin 314 Hz I t = with the general expression (see Equation 20.8) for the current in an ac circuit, 0 sin 2 I I f t π = , we see that ( 29 314 Hz 2 314 Hz or = 50.0 Hz 2 f t t f π π = = b. The resistance is equal to V r ms / I rms , where the rms-current is related to the peak current I 0 by rms 0 / 2 I I = . Thus, the resistance of the light bulb is 1
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( 29 2 rms rms 0 rms 2 120.0 V 2.40 10 0.707 A 2 V V R I I = = = = × (20.14) c. The average power is the product of the rms-current and rms-voltage: ( 29 0 rms rms rms 0.707 A 120.0 V 60.0 W 2 2 I P I V V = = = = (20.15a) 4. At what frequency does a 7.50- μ F capacitor have a reactance of 168 ?
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