A capacitor, a coil, and two resistors of equal resistance are arranged in an AC circuit as shown in Figure P33.66 (page 1028). An AC source provides an emf of ΔVrms = 20.0 V at a frequency of 60.0 Hz. When the double throw switch S is open as shown in the figure, the rms current is 183 mA. When the switch is closed in position a, the rms current is 298 mA. When the switch is closed in position b, the rms current is 137 mA. Determine the values of (a) R, (b) C, and (c) L. (d) Is more than one set of values possible? Explain.
(a)
The value of resistance.
Answer to Problem 33.66AP
The value of resistance is
Explanation of Solution
Given info: The value of the source emf is
The expression for inductive reactance is,
Here,
The expression for capacitive reactance is,
Here,
The expression for the impedance of the circuit is.
Here,
The expression of the impedance in terms of voltage and current is,
Here,
The figure below depicts the circuit when the switch is in open condition.
Figure (1)
From figure(1), for the throw switch in open condition:
Substitute
Substitute
For the throw switch at a position:
The two resistances are in parallel.
The expression of the equivalent resistance is.
Substitute
Substitute
Subtract equation (2) from equation (1).
Conclusion:
Therefore, the value of resistance is
(b)
The value of the capacitance.
Answer to Problem 33.66AP
The value of the capacitance is
Explanation of Solution
Given info: The value of the source emf is
The figure below depicts the circuit when switch is at position b.
Figure (2)
From figure (2), for the throw switch at b position:
When the switch is at position b the inductor gets short circuited.
Substitute
Rearrange the above expression for value of
Substitute
Substitute
Rearrange the above equation for value of value of
Substitute
Conclusion:
Therefore, the value of the capacitance is
(c)
The value of the inductance.
Answer to Problem 33.66AP
The values of the inductance are
Explanation of Solution
Given info: The value of the source emf is
Substitute
For first value of the inductor,
Substitute
Substitute
Thus, the first value of the inductor is
For second value of the inductor,
Substitute
Substitute for f in the above expression.
Thus, the second value of the inductor is
Conclusion:
Therefore, the values of the inductance are
(d)
Whether more than one set of value possible.
Answer to Problem 33.66AP
The resistance and capacitance has one set of values, the inductor has in two set of values.
Explanation of Solution
Given info: : The value of the source emf is
From the calculation in part (a),(b) and (c),
The value of resistance is
The value of capacitance is
The values of the inductor are
Hence the resistance and the capacitance has one value while the inductor has two set of value in the circuit.
Conclusion:
Therefore, the resistance and capacitance has one set of values, the inductor has in two set of values.
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Chapter 33 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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