An industrial load is modeled as a series combination of an inductor and a resistance as shown in Fig. 9.89. Calculate the value of a capacitor C across the series combination so that the net impedance is resistive at a frequency of 2 kHz.
Figure 9.89
Find the value of capacitor
Answer to Problem 89CP
When the net impedance is resistive at a frequency of
Explanation of Solution
Given data:
Refer to Figure 9.89 in the textbook.
The value of frequency
Formula used:
Write a general expression to calculate the impedance of a resistor.
Here,
Write a general expression to calculate the impedance of an inductor.
Here,
Write a general expression to calculate the impedance of a capacitor.
Here,
Write a general formula to calculate the angular frequency.
Here,
Calculation:
Refer to the given circuit, the value of resistor
In the given circuit, the series of combination of resistor and inductor is connected in parallel with the capacitor.
The equivalent impedance of the given circuit is written as follows using equations (1), (2) and (3).
Simplify the above equation as follows:
Simplify the above equation as follows:
The equivalent impedance must be resistive when
Equate the imaginary part of above equation to zero.
Simplify the above equation as follows:
Simplify the above equation to find
Substitute
Substitute
Simplify the above equation as follows:
Conclusion:
Thus, when the net impedance is resistive at a frequency of
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Chapter 9 Solutions
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