A coil has an inductance of 0.100 H and a resistance of 12.0 Ω. It is connected to a 110-V, 60.0-Hz line. Determine (a) the reactance of the coil, (b) the impedance of the coil, (c) the current through the coil, (d) the phase angle between current and supply voltage, (e) the power factor of the circuit, and (f) the reading of a wattmeter connected in the circuit.
(a)
The inductive reactance of the coil having inductance
Answer to Problem 27SP
Solution:
Explanation of Solution
Given data:
The value of inductance of the inductor is
The frequency of applied voltage is
Formula used:
The expression of inductive reactance of a coil is expressed as,
Here,
Explanation:
Recall the expression of inductive reactance.
Substitute
Conclusion:
The inductive reactanceof the coil is
(b)
The impedance of the coil having inductance
Answer to Problem 27SP
Solution:
Explanation of Solution
Given data:
The value of inductive reactance of the inductor is
The resistance of the coil is
Formula used:
The impedance of the coil is expressed as,
Here,
Explanation:
Recall the expression of impedance of the coil,
Substitute
Conclusion:
The impedance of the coil is
(c)
The current through the coil having inductance
Answer to Problem 27SP
Solution:
Explanation of Solution
Given data:
The rms value of voltage is
The impedance of the coil is
Formula used:
Write the expression of Ohm’s law for inductor in an ac circuit.
Here,
Explanation:
Recall the expressionof Ohm’s law.
Rearrange for
Substitute
Conclusion:
The current through the inductor is
(d)
The phase angle between current and supply voltage when
Answer to Problem 27SP
Solution:
Explanation of Solution
Given data:
The resistance of the coil is
The reactance of the coil is
Formula used:
The expression for phase angle between voltage and current in RL circuit is expressed as,
Here,
Explanation:
Recall the expressionfor phase angle between voltage and current.
Solve for
Substitute
Conclusion:
The circuit has inductive in nature; hence the voltage leads by
(e)
The power factor of the circuithaving the coilof inductance
Answer to Problem 27SP
Solution:
Explanation of Solution
Given data:
The phase angle between current and supply voltageis
Formula used:
The expression of the power factor is expressed as,
Here,
Explanation:
Recall the expression for power factor.
Substitute
Conclusion:
The power factor of the circuit is
(f)
The reading of wattmeter connected in the circuit across the coil having inductance
Answer to Problem 27SP
Solution:
Explanation of Solution
Given data:
The rms value of voltage is
The rms value of current is
The power factor of the circuit is
Formula used:
Power consumed in the circuit is calculated as,
Here,
Explanation:
Consider the expression for power consumed in the circuit.
Substitute
Conclusion:
The reading of wattmeter connected in 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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- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning