
Concept explainers
(a)
Find the value of the cutoff frequency in hertz for the RL low-pass filter shown in given figure.
(a)

Answer to Problem 1P
The value of the cutoff frequency
Explanation of Solution
Given data:
Refer to given figure in the textbook.
Formula used:
Write the expression to calculate the angular cutoff frequency.
Here,
Write the expression to calculate the cutoff frequency of the RL low-pass filter.
Here,
Calculation:
The given filter circuit is drawn as Figure 1.
Substitute
Simplify the above equation to find
Substitute
Rearrange the above equation to find
Conclusion:
Thus, the value of the cutoff frequency
(b)
Find the value of the transfer function
(b)

Answer to Problem 1P
The value of the transfer function
Explanation of Solution
Formula used:
Write the expression to calculate the impedance of the passive elements resistor and inductor.
Calculation:
The impedance circuit of the Figure 1 is drawn as Figure 2 using the equations (3) and (4).
Apply voltage division rule on Figure 2 to find
Rearrange the above equation to find
Substitute the equation (2) in above equation to find
Write the expression to calculate the transfer function of the circuit in Figure 2.
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus, the value of the transfer function
(c)
Find the steady state expression for the output voltage
(c)

Answer to Problem 1P
The steady state expression for the output voltage
Explanation of Solution
Given data:
The input voltage is,
Calculation:
From part (b),
Rearrange the above equation to find
The time domain expression for the above equation is written as,
Substitute
Substitute
Substitute
Simplify the above equation to find
Substitute
Substitute
Simplify the above equation to find
Substitute
Substitute
Simplify the above equation to find
Conclusion:
Thus, the steady state expression for the output voltage
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Chapter 14 Solutions
Electric Circuits, Global Edition
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