For a certain source-free parallel RLC circuit, R = 1 kΩ, C = 3 μF, and L is such that the circuit response is overdamped. (a) Determine a suitable value of L. (b) Write the equation for the voltage v across the resistor if it is known that v(0−) = 9 V and dv/dt|t=0+ = 2 V/s.
(a)
Find inductor
Answer to Problem 1E
The value of inductor
Explanation of Solution
Given data:
Value of resistance
Value of capacitor
Formula used:
The expression for the two solutions of the characteristic equation of a parallel
Here,
The value of real part of root of natural response of the source free parallel
The value of imaginary part of root of natural response of the source free parallel
The expression for over damped source free response of parallel
Calculation:
Substitute
Substitute
Substitute
Squaring both the sides,
Conclusion:
Thus, the value of inductor
(b)
Find equation for voltage across resistor.
Answer to Problem 1E
The voltage across resistor is
Explanation of Solution
Given data:
Value of initial voltage
Value of rate of change of voltage for
Calculation:
Choose the value of inductor
The general form of natural response for parallel
Here,
Differentiate both sides of equation (6) with respect to time:
The expression for the voltage across resistor
Substitute
Rearrange for
Substitute
Substitute
Solve for
Substitute
Solve for
Substitute
Substitute
Solve for
Rearrange for
Substitute
Substitute
The voltage across resistor is same as the voltage
Conclusion:
Thus, the voltage across resistor is
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Chapter 9 Solutions
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