If is(t) = 7.5e–2t u(t) A in the circuit shown in Fig. 16.40, find the value of io(t).
Find the expression of current
Answer to Problem 17P
The expression of current
Explanation of Solution
Given data:
Refer to Figure 16.40 in the textbook.
The value of source current is,
Formula used:
Write a general expression to calculate the impedance of a resistor in s-domain.
Here,
Write a general expression to calculate the impedance of an inductor in s-domain.
Here,
Write a general expression to calculate the impedance of a capacitor in s-domain.
Here,
Calculation:
The given circuit is redrawn as shown in Figure 1.
Substitute
Substitute
Substitute
Apply Laplace transform for equation (1) to find
Convert the Figure 1 into s-domain as shown in Figure 2.
Apply nodal analysis at node
Simplify the above equation to find
From the above equation , the characteristic equation is
Write a general expression to calculate the roots of quadratic equation
Comparing the equation (6) with the equation
Substitute
Simplify the above equation to find
Substitute the roots of characteristic equation in equation (5) to find
Refer to Figure 2, the current through the capacitor is calculated as follows:
Substitute
Take partial fraction for above equation.
The equation (8) can be written as follows:
Simplify the above equation as follows:
Substitute
Simplify the above equation as follows:
Simplify the above equation to find
Substitute
Simplify the above equation to find
Substitute
Simplify the above equation to find
Substitute
Take inverse Laplace transform for above equation to find
Simplify the above equation to find
Simplify the above equation to find
Conclusion:
Thus, the expression of current
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Chapter 16 Solutions
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