The expression for average power supplied.
Answer to Problem 58PQ
The expression for average power supplied is
Explanation of Solution
Write the expression for average power.
Here,
Write the expression for current to the circuit connected to an alternating source of emf.
Here,
Write the expression for emf in the circuit.
Here,
Write the expression for energy dissipated in time
Substitute
Substitute
Integrate the expression between the limits
Now,
Substitute,
The above expression can be rewritten as.
Also, rms value of current is given by.
Here,
And,
The rms value of emf is given by.
Here,
Substitute
Therefore, the expression for average power supplied is
Want to see more full solutions like this?
Chapter 33 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- (a) What is the resistance of a light bulb that uses an average power of 75.0 W when connected to a 60.0-Hz power source having a maximum voltage of 170. V? (b) What is the resistance of a 100.-W lightbulb?arrow_forwardIn an oscillating LC circuit, L = 8.00 mH and C = 1.40 mF.At time t = 0, the current is maximum at 12.0 mA. (a) What is the maximum charge on the capacitor during the oscillations? (b) At what earliest time t > 0 is the rate of change of energy in the capacitor maximum? (c) What is that maximum rate of change?arrow_forwardA sinusoidal voltage Δv = 35.0 sin(100t), where Δv is in volts and t is in seconds, is applied to a series RLC circuit with L = 180 mH, C = 99.0 µF, and R = 67.0 Ω. (a) What is the impedance (in Ω) of the circuit? (b)What is the maximum current (in A)? (c)Determine the numerical value for ? (in rad/s) in the equation i = Imax sin(?t − ?).rad/s (d)Determine the numerical value for ? (in rad) in the equation i = Imax sin(?t − ?). rad (e) What If? For what value of the inductance (in H) in the circuit would the current lag the voltage by the same angle ? as that found in part (d)? H (f)What would be the maximum current (in A) in the circuit in this case? please fill the whole thing thank you.arrow_forward
- A 25-μF capacitor is connected to an emf given by v(t) = (160 V) sin (120πt) . (a) What is the reactance of the capacitor? (b)Write an expression for the current output of the source.arrow_forwardA sinusoidal voltage Δv = 45.0 sin(100t), where Δv is in volts and t is in seconds, is applied to a series RLC circuit with L = 170 mH, C = 99.0 µF, and R = 60.0 Ω. a) What is the impedance (in Ω) of the circuit? b) What is the maximum current (in A)? c) Determine the numerical value for ? (in rad/s) in the equation i = Imax sin(?t − ?). d) Determine the numerical value for ? (in rad) in the equation i = Imax sin(?t − ?). e) What If? For what value of the inductance (in H) in the circuit would the current lag the voltage by the same angle ? as that found in part (d)? f) What would be the maximum current (in A) in the circuit in this case?arrow_forwardA 24.0 nF capacitor is connected across an AC generator that produces a peak voltage of 5.90 V. a. At what frequency f is the peak current 60.0 mA ? b. What is the instantaneous value of the emf at the instant when iC =IC?arrow_forward
- A sinusoidal voltage Δv = (80.0 V) sin (150t) is applied to aseries RLC circuit with L = 80.0 mH, C = 125.0 µF, and R =40.0 Ω. (a) What is the impedance of the circuit? (b) What isthe maximum current in the circuit?arrow_forwardAn ac generator with emf em sin vdt, where m e=25.0 V and vd 377 rad/s, is connected to a 4.15 mF capacitor. (a)What is the maximum value of the current? (b) When the current is a maximum, what is the emf of the generator? (c)When the emf of the generator is -12.5 V and increasing in magnitude, what is the current?arrow_forwardIn an L-C circuit, L = 85.0 mH and C = 3.20 uF. During the oscillations the maximum current in the inductor is 0.850 mA. (a) What is the maximum charge on the capacitor? (b) What is the magnitude of the charge on the capacitor at an instant when the current in the inductor has magnitude 0.500 mA?arrow_forward
- (a) Show the voltage waveforms across each half of the secondary winding and across RL when a 100 V peak sine wave is applied to the primary winding in Figure.(b) what is Vavg and fout if fin = 50 Hz?arrow_forwardIn an oscillating LC circuit, L = 25.0 mH and C = 7.80 mF. At time t 0 the current is 9.20 mA, the charge on the capacitor is 3.80 mC, and the capacitor is charging.What are (a) the total energy in the circuit, (b) the maximum charge on the capacitor, and (c) the maximum current? (d) If the charge on the capacitor is given by q = Q cos(vt + f), what is the phase angle f? (e) Suppose the data are the same, except that the capacitor is discharging at t = 0.What then is f?arrow_forwardA 1.50 mF capacitor has a capacitive reactance of 12.0 ohm. (a) What must be its operating frequency? (b) What will be the capacitive reactance if the frequency is doubled?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning