Concept explainers
Assuming an operating frequency of 50 Hz, compute the instantaneous voltage at t = 10 ms and t = 25 ms for each of the phasor quantities represented in Exercise 28.
(a)
Find the instantaneous voltage of
Answer to Problem 29E
The instantaneous voltage of
Explanation of Solution
Given data:
Formula used:
Consider the Euler’s identity,
Consider the general expression for voltage response.
The complex form of voltage response is,
Calculation:
Simplify equation (1) as follows.
Consider the general expression for frequency in terms of
Substitute
The cosine function of phasor expression
Substitute
Simplify the equation as follows.
Substitute
Simplify the equation as follows.
Conclusion:
Thus, the instantaneous voltage of
(b)
Find the instantaneous voltage of
Answer to Problem 29E
The instantaneous voltage of
Explanation of Solution
Given data:
Calculation:
Simplify equation (3) as follows.
The cosine function of phasor expression
Substitute
Simplify the equation as follows.
Substitute
Simplify the equation as follows.
Conclusion:
Thus, the instantaneous voltage of
(c)
Find the instantaneous voltage of
Answer to Problem 29E
The instantaneous voltage of
Explanation of Solution
Given data:
Calculation:
Simplify equation (5) as follows.
The cosine function of phasor expression
Substitute
Simplify the equation as follows.
Substitute
Simplify the equation as follows.
Conclusion:
Thus, the instantaneous voltage of
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