Using Fig. 9.45, design a problem to help other students better understand admittance.
Figure 9.45
Design a problem to make better understand about the admittance using Figure 9.45.
Explanation of Solution
Problem design:
Determine the value of current
Formula used:
Write the expression to convert the time domain expression into phasor domain.
Here,
A is the magnitude,
t is the time, and
Write the expression to calculate the impedance of the passive elements resistor, inductor and capacitor.
Here,
Calculation:
(a)
The Figure 9.45(a) is redrawn as Figure 1 by assuming the values for the respective elements.
Refer to Figure 1, the current equation is,
Here, angular frequency
Use the equation (1) to express the above equation in phasor form.
Substitute
Substitute
The Figure 1 is redrawn as impedance circuit in the following Figure 2.
Apply current division rule on Figure 2 to find
Substitute
Use the equation (1) to express the above equation in time domain form.
Substitute
Refer to Figure 2, the voltage across the impedance
Substitute
Use the equation (1) to express the above equation in time domain form.
Substitute
Therefore, the value of current
(b)
The Figure 9.45(b) is redrawn as Figure 3 by assuming the values for the respective elements.
Refer to Figure 3, the voltage equation is,
Here, angular frequency
Use the equation (1) to express the above equation in phasor form.
Substitute
Substitute
Substitute
Substitute
The Figure 3 is redrawn as impedance circuit in the following Figure 4.
Refer to Figure 4, the impedances
Write the expression to calculate the equivalent impedance of the series connected impedances
Refer to Figure 4, the source voltage
Write the expression to calculate the current
Substitute
Substitute
Use the equation (1) to express the above equation in time domain form.
Substitute
Apply voltage division rule on Figure 4 to find
Substitute
Use the equation (1) to express the above equation in time domain form.
Substitute
Therefore, the value of current
Conclusion:
Thus, the problem to make better understand about the admittance using Figure 9.45 is designed.
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