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
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Chapter 35 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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