Concept explainers
Consider the circuit represented in Fig. 13.53. The coupling coefficient k = 0.75. If is = 5 cos 200t mA, calculate the total energy stored at t = 0 and t = 5 ms if (a) a-b is open-circuited (as shown); (b) a-b is short-circuited.
FIGURE 13.53
(a)
Find the total energy stored in the system at
Answer to Problem 27E
The total energy stored in the system at
Explanation of Solution
Given data:
Refer to Figure 13.53 in the textbook for the given circuit.
The terminals a-b in the given circuit are open circuited.
Formula used:
Write the expression for energy stored in the magnetic field due to self-inductance of the coil at an instant of time as follows:
Here,
Calculation:
As the terminals a-b in the given circuit are open circuited, the current through the secondary winding loop is 0 A. Therefore, the total energy stored in the system is only due to the primary coils of the given circuit.
From the given circuit, find the value of inductance of primary coil when the terminals a-b in the given circuit are open circuited as follows:
Find the current through the primary coil at
Modify the expression in Equation (1) for energy stored in the system due to the coil
Substitute
Find the current through the primary coil at
Modify the expression in Equation (1) for energy stored in the system due to the coil
Substitute
Conclusion:
Thus, the total energy stored in the system at
(b)
Find the total energy stored in the system at
Answer to Problem 27E
The total energy stored in the system at
Explanation of Solution
Given data:
The terminals a-b in the given circuit are short-circuited.
Formula used:
Write the expression for energy stored in the magnetic field due to mutual inductance of the coils at an instant of time as follows:
Here,
Write the expression for mutual inductance in terms of self-inductance of primary and secondary coils as follows:
Here,
Calculation:
Substitute
From the given circuit, find the current
Substitute
Simplify the expression as follows:
Find the current through the secondary coil at
From Part (a), the energy stored in the system due to the coil
Modify the expression in Equation (1) for energy stored in the system due to the coil
Substitute
Rearrange the expression in Equation (2) to find the energy stored in the magnetic field due to the mutual inductance of the coils at
Substitute
Write the expression for total energy stored in the system at
Substitute
From Part (a), the energy stored in the system due to the coil
Find the current through the secondary coil at
Modify the expression in Equation (1) for energy stored in the system due to the coil
Substitute
Rearrange the expression in Equation (2) to find the energy stored in the magnetic field due to the mutual inductance of the coils at
Substitute
Modify the expression in Equation (4) for total energy stored in the system at
Substitute
Conclusion:
Thus, the total energy stored in the system at
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Chapter 13 Solutions
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