1 of 6 4/28/2010 2:12 PM

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1 1 of 6 4/28/2010 2:12 PM Chapter 36 Homework Due: 8:00am on Wednesday, April 28, 2010 Note: To understand how points are awarded, read your instructor's Grading Policy [Return to Standard Assignment View] Alternating Voltages and Currents The voltage supplied by a wall socket varies with time, reversing its polarity with a constant frequency, as shown in the graph What is the rms value of the voltage plotted in the graph? Hint A1 RMS value of a quantity with sinusoidal time dependence A quantity that varies with time as (or ) has a maximum value equal to and an rms value given by Hint A2 Find the maximum value of the voltage Express your answer in volts = 120 This is the standard rms voltage supplied to a typical household in North America When a lamp is connected to a wall plug, the resulting circuit can be represented by a simplified AC circuit, as shown in the figure Here the lamp has been replaced by a resistor with an equivalent resistance = 120 What is the rms value of the current flowing through the circuit? Hint B1 Ohm's law in AC circuits Ohm's law can still be applied to an AC circuit, provided the values used to describe all physical quantities are consistent For example, Ohm's law can be written using maximum values of voltage and current, or alternatively using rms quantities Express your answer in amperes = 100 What is the average power dissipated in the resistor? Hint C1 Average power in an AC circuit Express your answer in watts = 120 The instantaneous power dissipated in the resistor can be substantially higher than the average power However, since the voltage supplied to the resistor varies in time, so does the instantaneous power Therefore, a better estimate of the energy dissipated in an AC circuit is given by the average power For example, the power rating on light bulbs is in fact the average power dissipated in the bulb Problem 367

2 2 of 6 4/28/2010 2:12 PM A 065 capacitor is connected across an AC generator that produces a peak voltage of 23 What is the peak current to and from the capacitor if the emf frequency is 100? Express your answer using two significant figures = What is the peak current to and from the capacitor if the emf frequency is 100? Express your answer using two significant figures = 92 A high-pass filter with a crossover frequency of 1000 Hz uses a resistor Problem 3614 What is the value of the capacitor? 159 Determining Inductance from Voltage and Current An inductor is hooked up to an AC voltage source The voltage source has EMF and frequency The current amplitude in the inductor is What is the reactance Hint A1 of the inductor? Definition of reactance Express your answer in terms of and = What is the inductance of the inductor? Hint B1 Reactance in terms of and Express your answer in terms of,, and = What would happen to the amplitude of the current in the inductor if the inductance were doubled? Hint C1 How to approach the problem There would be no change in the amplitude of the current The amplitude of the current would be doubled The amplitude of the current would be halved The amplitude of the current would be quadrupled Problem 3620 An inductor is connected to a 15 khz oscillator The peak current is 65 ma when the rms voltage is 60 V What is the value of the inductance?

3 3 of 6 4/28/2010 2:12 PM 139 mh Problem 3652 In the figure, what is the current supplied by the emf when the frequency is very small? 0100 A What is the current supplied by the emf when the frequency is very large? 0200 A Learning Goal: To understand basic calculations involving L-R-C ac circuits L-R-C AC Circuits Because the currents and voltages vary, ac circuits are more complex than dc circuits Consider a circuit consisting of a resistor of resistance, an inductor of inductance, and a capacitor of capacitance connected in series to an ac power source As with all circuit components connected in series, the same current flows through each of these elements This is an ac circuit, so the current is changing with time The current at a time can be found using the relationship:, where is the maximum current and ( is the frequency of the current source) The relationship between the current and voltage in an ac circuit works according to Ohm's law Consider just the resistor in the circuit Because the current changes in time, the voltage across the resistor also changes However, both and will be at a maximum at the same time The maximum voltage across the resistor is given by Recall that an inductor is designed to oppose any change in current in the circuit Although an inductor has no resistance, there is a potential difference and do not reach maximum values at the same time The voltage reaches a maximum before the current across the ends of the inductor Unlike the case for the resistor, The maximum potential difference across the inductor is By defining the quantity as the inductive reactance, can be rewritten as This equation is similar to Ohm's law An L-R-C circuit, operating at 60, has an inductor with an inductance of, a capacitance of, and a resistance of 0329 What is the inductive reactance of this circuit? Hint A1 Find Enter your answer numerically in ohms = 0577 Because is proportional to the frequency, low-frequency ac currents pass through an inductor more easily than high-frequency ac currents Hence circuits containing inductors are often used as filters that allow low frequencies but not high frequencies to pass These filters are called low-pass filters A capacitor is designed to store energy by allowing charge to build up on its plates Although a capacitor has no resistance in an ac circuit, there is a potential difference maximum values of and do not occur at the same time The voltage reaches a maximum after the current across the plates of the capacitor The The maximum potential difference across the inductor is By defining the quantity as the capacitive reactance, can be rewritten as As with the case for the inductor, this equation is similar to Ohm's law

4 4 of 6 4/28/2010 2:12 PM What is the capacitive reactance of the circuit in? Enter your answer numerically in ohms = 0159 Because is inversely proportional to the frequency, high-frequency ac currents pass through a capacitor more easily than low-frequency ac currents Hence circuits containing capacitors are often used as filters that allow high frequencies but not low frequencies to pass These filters are called high-pass filters The capacitive reactance, the inductive reactance, and the resistance of the circuit can be combined to give the impedance of the circuit The impedance is a measure of the total reactance and resistance of the circuit and is similar to the equivalent resistance that can be found from various resistors in a dc circuit Because and do not reach maximum values at the same time as, the impedance is not found by adding,, and Instead, the impedance is found using The analogy to Ohm's law is then What is the total impedance of the circuit in Parts A and B? Enter your answer numerically in ohms = 0532 In ac circuits, and are not measured directly Instead, ac ammeters and voltmeters are designed to measure the root-mean-square values of and :, which can be used in the equation to yield Part D If this circuit were connected to a standard 120 ac outlet, what would the rms current in the circuit be? Enter your answer numerically in amperes = 226 The current is high because the total impedance is relatively low Actually, plugging such a circuit into a 120- outlet would most likely burn out the circuit elements A frequent application of L-R-C ac circuits is the tuning mechanism in a radio The L-R-C ac circuit will have a resonant frequency that depends on both the inductance and capacitance of the circuit according to the formula This is the frequency at which the impedance is the smallest, which causes the largest current to appear in the circuit for a given The radio picks up this resonant frequency and suppresses signals at other frequencies A variable capacitor in this circuit causes the resonant frequency of the circuit to change When you tune the radio you are adjusting the value of the capacitance in the circuit and hence the resonant frequency Part E To see whether the L-R-C ac circuit from would be suitable for a tuner in a radio, find the resonant frequency of this circuit Enter your answer numerically in hertz = 315 This frequency does not correspond to either the standard AM or FM band Average Power in an L-R-C Circuit A circuit consists of a resistor (resistance ), inductor (inductance ), and capacitor (capacitance ) connected in series with an AC source supplying sinusoidal voltage Assume that all circuit elements are ideal, so that the only resistance in the circuit is due to the resistor Also assume that is the resonant frequency of the circuit What is the average power supplied by the voltage source? Hint A1 Hint A2 Find the instantaneous power Average value of a periodic function

5 5 of 6 4/28/2010 2:12 PM Express your answer in terms of any or all of the following quantities:,,, and = Problem 3629 The heating element of a hair drier dissipates 1560 W when connected to a 120 V/60 Hz power line What is its resistance? 923 Problem 3649 A series RLC circuit consists of a 105 resistor, a 0100 inductor, and a 210 capacitor It is attached to a 120 V/60 Hz power line What is the peak current? 124 A What is the phase angle? -402 What is the average power loss? 801 Answer Requested W Resonating RLC Series Circuit Ranking Task Six series RLC circuits are described below, where is the resistance, the inductance, and the capacitance of the circuits Rank these circuits on the basis of their resonance frequencies Hint A1 Hint A2 Hint A3 Resonance and the phase between voltage and current Resonance and impedance Equating inductive and capacitive reactance at resonance Rank from largest to smallest To rank items as equivalent, overlap them View Each circuit is driven at its resonance frequency by a 100 AC power supply Rank these circuits on the basis of their maximum current Hint B1 Current at resonance

6 6 of 6 4/28/2010 2:12 PM Hint B2 Maximizing maximum current Rank from largest to smallest To rank items as equivalent, overlap them View Problem 3663 A motor attached to a 120 V/60 Hz power line draws an 810 A current Its average energy dissipation is 760 W What is the power factor? 0782 What is the rms resistor voltage? 938 V What is the motor's resistance? 116 Part D How much series capacitance needs to be added to increase the power factor to 10? 287 Score Summary: Your score on this assignment is 109% You received 7179 out of a possible total of 75 points, plus 995 points of extra credit