A 10.0-µF capacitor is in series with a 40.0-Ω resistance, and the combination is connected to a 110-V, 60.0-Hz line. Calculate (a) the capacitive reactance, (b) the impedance of the circuit, (c) the current in the circuit, (d) the phase angle between current and supply voltage, and (e) the power factor for the circuit.
(a)
The capacitive reactance of the
Answer to Problem 28SP
Solution:
Explanation of Solution
Given data:
The value of capacitance of the capacitor is
The frequency of applied voltage is
Formula used:
The expression of capacitive reactance is expressed as,
Here,
Explanation:
Consider the expression of capacitive reactance,
Substitute
Conclusion:
The capacitive reactance of the capacitor is
(b)
The impedance of the RC circuit having
Answer to Problem 28SP
Solution:
Explanation of Solution
Given data:
The value of capacitive reactance of the capacitor is
The resistance of the RC circuit is
Formula used:
The impedance of the capacitor is expressed as,
Here,
Explanation:
Consider the expression of impedance of the RC circuit.
Substitute
Conclusion:
The impedance of the RC circuit is
(c)
The current in the RC circuit having
Answer to Problem 28SP
Solution:
Explanation of Solution
Given data:
The rms value of voltage is
The impedance of the RC circuit is
Formula used:
Write the expression of Ohm’s law for ac circuit.
Here,
Explanation:
Consider the expressionof Ohm’s law.
Rearrange for
Substitute
Conclusion:
The current through thecircuit is
(d)
The phase angle between current and supply voltage when the
Answer to Problem 28SP
Solution:
Voltage lags by
Explanation of Solution
Given data:
The resistance of the circuit is
The value of capacitive reactance of the inductor is
Formula used:
The expression for phase angle between voltage and current in RL circuit is expressed as,
Here,
Explanation:
Consider the expressionfor phase angle between voltage and current.
Solve for
Substitute
The circuit is capacitive in nature; hence voltage is lagging in nature.
Conclusion:
The phase angle between current and supply voltage is
(e)
The power factor of the circuit when the
Answer to Problem 28SP
Solution:
Explanation of Solution
Given data:
The phase angle between current and supply voltage is
Formula used:
The expression of the power factor is expressed as,
Here,
Explanation:
Consider the expression for power factor.
Substitute
Conclusion:
The power factor of the circuit is
Want to see more full solutions like this?
Chapter 35 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
- A 1.5k resistor and 30-mH inductor are connected in series, as below, across a120-V(rms)ac power source oscillating at 60-Hz frequency. (a) Find the current in the circuit. (b) Find the voltage drops across the resistor and inductor. (C) Find the impedance of the circuit. (d) Find the power dissipated in the resistor. (e) Find the power dissipated in the inductor. (1) Find the power produced by the source.arrow_forwardAt 1000 Hz, the reactance of a 5.0-mH inductor is equal to the reactance of a particular capacitor. What is the capacitance of the capacitor?arrow_forwardFor an RLC series circuit, the voltage amplitude and frequency of the source are 100 V and 500 Hz, respectively; R=500 ; and L = 0.20H . Find the average power dissipated in the resistor for the following values for the capacitance: (a) C=2.0F and (b) C=2.0F .arrow_forward
- A 700-pF capacitor is connected across an ac source with a voltage amplitude of 160 V and a frequency of 20 kHz. (a) Determine the capacitive reactance of the capacitor and the amplitude of the output current of the source. (b) If the frequency is changed to 60 Hz while keeping the voltage amplitude at 160 V, what are the capacitive reactance and the current amplitude?arrow_forwardAn LC circuit in an AM tuner (in a car stereo) uses a coil with an inductance of 2.5 mH and a variable capacitor. If the natural frequency of the circuit is to be adjustable over the range 540 to 1600 kHz (the AM broadcast band), that range of capacitance is required?arrow_forwardCalculate the reactance of a 5.0F capacitor at (a) 60 Hz, (b) 600 Hz, and (c) 6000 Hz.arrow_forward
- In an ideal AC circuit with capacitance, there is no resistance. Is any energy dissipated? How about in a real AC circuit with capacitance?arrow_forwardA series RLC circuit has resistance R = 50.0 and inductance L. = 0.500 H. (a) Find the circuits capacitance C if the voltage source operates at a frequency of f = 60.0 Hz and the impedance is Z = R = 50.0 . (b) What is the phase angle between the current and the voltage?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
- College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning