Find the expression of voltage
Answer to Problem 8P
The expression of voltage
Explanation of Solution
Given data:
A branch voltage in an
The value of initial voltage
The value of
Calculation:
Apply Laplace transform for equation (1) with initial conditions.
Simplify the above equation as follows.
Substitute
Simplify the above equation to find
From equation (3), the characteristic equation is written as follows,
Write an expression to calculate the roots of characteristic equation
Here,
Compare equation (4) with quadratic equation
Substitute
Now, the equation (3) is written as follows.
Take partial fraction for equation (6).
The equation (7) can be written as follows.
Simplify the above equation.
Substitute
Simplify the above equation as follows.
Simplify the above equation to find
Substitute
Simplify the above equation as follows.
Simplify the above equation to find
Multiply and divide by
Simplify the above equation to find
Substitute
Simplify the above equation as follows.
Simplify the above equation to find
Multiply and divide by
Simplify the above equation to find
Substitute
Apply inverse Laplace transform for equation (9) to find
Simplify the above equation to find
Simplify the above equation to find
Conclusion:
Thus, the expression of voltage
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Chapter 16 Solutions
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