Assuming the passive sign convention and an operating frequency of 314 rad/s, calculate the phasor voltage V which appears across each of the following when driven by the phasor current : (a) a 2 Ω resistor; (b) a 1 F capacitor; (c) a 1 H inductor; (d) a 2 Ω resistor in series with a 1 F capacitor; (e) a 2 Ω resistor in series with a 1 H inductor. (f) Calculate the instantaneous value of each voltage determined in parts (a) to (e) at t = 0.
(a)
Find the phasor voltage across
Answer to Problem 33E
The phasor voltage across
Explanation of Solution
Given data:
Formula used:
Consider the expression of phasor voltage across resistor.
Here,
Calculation:
Substitute
Conclusion:
Thus, the phasor voltage across
(b)
Find the phasor voltage across
Answer to Problem 33E
The phasor voltage across
Explanation of Solution
Formula used:
Consider the expression of phasor voltage across capacitor.
Here,
Calculation:
Substitute
Conclusion:
Thus, the phasor voltage across
(c)
Find the phasor voltage that developed across
Answer to Problem 33E
The phasor voltage that developed across
Explanation of Solution
Formula used:
Consider the expression of phasor voltage across inductor.
Here,
Calculation:
Substitute
Conclusion:
Thus, the phasor voltage that developed across
(d)
Find the phasor voltage across series connected
Answer to Problem 33E
The phasor voltage across a series connected
Explanation of Solution
Calculation:
Find total voltage across a series connected
Substitute
Conclusion:
Thus, the phasor voltage across a series connected
(e)
Find the phasor voltage across series connected
Answer to Problem 33E
The phasor voltage across a series connected
Explanation of Solution
Calculation:
Find total voltage across a series connected
Substitute
Conclusion:
Thus, the phasor voltage across a series connected
(f)
Find the instantaneous value of each voltage obtained in parts (a) to (e) at
Answer to Problem 33E
The instantaneous value of each voltage obtained in parts (a) to (e) at
Explanation of Solution
Formula used:
Consider the general expression for voltage response.
The complex form of voltage response is,
Calculation:
Part (a):
The phasor voltage across
The instantaneous voltage across
Part (b):
The phasor voltage across
The instantaneous voltage across
Part (c):
The phasor voltage across
The instantaneous voltage across
Part (d):
The phasor voltage across a series connected
The instantaneous voltage across series connected
Part (e):
The phasor voltage across a series connected
The instantaneous voltage across series connected
Conclusion:
Thus, the instantaneous value of each voltage obtained in parts (a) to (e) at
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Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
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