In the circuit of Fig. 9.47, find io when:
- (a) ω = 1 rad/s
- (b) ω = 5 rad/s
- (c) ω = 10 rad/s
Figure 9.47
(a)
Find the value of the current
Answer to Problem 40P
The value of the current
Explanation of Solution
Given data:
Refer to Figure 9.47 in the textbook.
The value of the angular frequency
Formula used:
Write the expression to calculate the impedance of the passive elements resistor, inductor and capacitor.
Here,
Calculation:
The given circuit is redrawn as Figure 1.
Refer to Figure 1, the current equation is,
Convert the given current into phasor form.
Substitute
Substitute
Substitute
Substitute
The Figure 1 is redrawn as impedance circuit in the following Figure 2.
Write the expression to obtain the source transformation from current to voltage.
Substitute
Based upon the source transformation, the Figure 2 is reduced as the following Figure3.
Refer to Figure 3, the series connected impedances
Therefore, the total equivalent impedance is calculated as follows.
Substitute
Substitute
Substitute
The reduced circuit of Figure 3 is drawn as Figure 4.
Refer to Figure 4, the current
Substitute
Convert the above equation from phasor form to time domain form.
Substitute
Conclusion:
Thus, the value of the current
(b)
Find the value of the current
Answer to Problem 40P
The value of the current
Explanation of Solution
Given data:
The value of the angular frequency
Calculation:
Substitute
Substitute
Substitute
Refer to Figure 4, the current
Substitute
Convert the above equation from phasor form to time domain form.
Substitute
Conclusion:
Thus, the value of the current
(c)
Find the value of the current
Answer to Problem 40P
The value of the current
Explanation of Solution
Given data:
The value of the angular frequency
Calculation:
Substitute
Substitute
Substitute
Refer to Figure 4, the current
Substitute
Convert the above equation from phasor form to time domain form.
Substitute
Conclusion:
Thus, the value of the current
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Chapter 9 Solutions
Fundamentals of Electric Circuits
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