Concept explainers
For the circuit in Fig. 7.100,
v = 90e−50t V
and
i = 30e−50t A, t > 0
- (a) Find L and R.
- (b) Determine the time constant.
- (c) Calculate the initial energy in the inductor.
- (d) What fraction of the initial energy is dissipated in 10 ms?
Figure 7.100
(a)
Find the value of resistance R and inductance L in the Figure 7.100.
Answer to Problem 20P
The value of resistance R in the circuit is
Explanation of Solution
Given data:
The voltage
The current
Formula used:
Write the expression to find the voltage across the inductor for the given circuit.
Here,
L is the inductance of the inductor.
Write the expression to find the time constant for RL circuit.
Here,
R is the resistance of the resistor.
Write the general expression to find the voltage response in the RL Circuit.
Here,
Calculation:
Substitute
Rearrange the equation as follows,
Convert the unit H to mH.
Compare the given voltage
Rearrange the equation (4) to find the time constant
Substitute
Rearrange the equation (5) to find the resistance R in ohms.
Conclusion:
Thus, the value of resistance R in the circuit is
(b)
Find the time constant
Answer to Problem 20P
The time constant
Explanation of Solution
Given data:
Refer to part (a).
The value of resistance R is
The value of inductance L is
Calculation:
Substitute
Substitute the units
Convert the unit s to ms.
Conclusion:
Thus, the time constant
(c)
Find the value of initial energy stored in the inductor.
Answer to Problem 20P
The value of initial energy stored in the inductor is
Explanation of Solution
Given data:
Refer to part (a).
The value of inductance L is
Formula used:
Write the expression to find the energy stored in the inductor.
Here,
Calculation:
The given current is,
The initial current in the RL circuit at
Substitute
Conclusion:
Thus, the value of initial energy stored in the inductor is
(d)
Find the fraction of the energy dissipated in the first 10 ms.
Answer to Problem 20P
The fraction of the energy dissipated in the first 10 ms is
Explanation of Solution
Given data:
Refer to part (c).
The value of initial energy w stored in the inductor is
Formula used:
Write the expression to find the energy stored in the inductor.
Calculation:
The given current is,
The current in the RL circuit at
Substitute
The fraction of the energy dissipated in the first 10 ms is calculated as follows.
Substitute
Conclusion:
Thus, the fraction of the energy dissipated in the first 10 ms is
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Chapter 7 Solutions
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