Concept explainers
The inductors in Fig. 6.87 are initially charged and are connected to the black box at t = 0. If i1(0) = 4 A, i2(0) = −2 A, and v(t) = 50e−200t mV, t ≥ 0, find:
- (a) the energy initially stored in each inductor,
- (b) the total energy delivered to the black box from t = 0 to t = ∞,
- (c) i1(t) and i2(t), t ≥ 0,
- (d) i(t), t ≥ 0.
Figure 6.87
For Prob. 6.65.
(a)
Calculate the initial energy stored in each inductor for the given initial conditions.
Answer to Problem 65P
The energy stored initially in each inductor
Explanation of Solution
Given data:
The Black box connects across the initially charged inductors at
The initial current of inductor
The initial current of inductor
The voltage across the inductors and black box is same. That is,
Formula used:
Write the formula to find the energy stored in an inductor.
Calculation:
Re-draw the given figure as shown in Figure 1.
Using the formula in equation (1), the energy stored initially in inductor
Substitute
Using the formula in equation (1), the energy stored initially in inductor
Substitute
Conclusion:
Thus, the energy stored initially in each inductor
(b)
Calculate the total energy delivered to the black box by the inductors for
Answer to Problem 65P
The total energy delivered to the black box by the inductors is
Explanation of Solution
Given data:
Refer to Part (a).
Formula used:
Write the formula to find the total energy delivered to the black box by the inductors from
Here,
Calculation:
The total energy delivered to the black box in period of
Substitute
Conclusion:
Thus, the total energy delivered to the black box by the inductors is
(c)
Calculate the currents in each inductor for the period of
Answer to Problem 65P
The currents
Explanation of Solution
Given data:
Refer to Part (a).
Formula used:
Write the formula to find the current through an inductor.
Here,
Calculation:
Using the formula in equation (3), the current through an inductor
Since the black box and both inductors are in parallel,
Substitute
In the Figure 1, currents
From Figure 2, the current
Substitute
Reduce the equation as follows.
Using the formula in equation (3), the current
Substitute
Consider reversing polarities for voltage
Substitute
Reduce the equation as follows.
Conclusion:
Thus, the currents
(d)
Find the current
Answer to Problem 65P
The current
Explanation of Solution
Given data:
Refer to part (a).
Formula used:
Write the formula for the current
Here,
Calculation:
Refer to part (c), the currents
Substitute
Conclusion:
Thus, the current
Want to see more full solutions like this?
Chapter 6 Solutions
Fundamentals of Electric Circuits
- A 140-mH inductor and a 5.10-n resistor are connected with a switch to a 6.00-V battery as shown in the figure below. Wele R L (a) After the switch is first thrown to a (connecting the battery), what time interval elapses before the current reaches 220 mA? ms (b) What is the current in the inductor 10.0 s after the switch is closed? | A (C) Now the switch is quickly thrown from a to b. What time interval elapses before the current in the inductor falls to 160 mA? msarrow_forwardThe R-L Circuit: An inductor with an inductance of 2.50 H and a resistance of 7.00 n is connected to the terminals ofa battery with an emf of 6.00 V and an internal resistance of 1.00 n. What is the rate ofincrease of current at the instant when the current is 0.500 A? A) 0.8 A/s B) 0.6 A/s C) 0.4 A/s D) zero E) None of the above.arrow_forwardAt t= 0, a 2.3 uF capacitance is pre-charged to an unknown voltage V. The capacitance is in parallel with a 4 k2 resistance. For t>0 the capacitor is disconnected from the charging source and allowed to discharge into the resistor. At t = 2 ms, the voltage across the capacitance is 10 V. Calculate the value of V (V).arrow_forward
- An (open) electric circuit consists of an inductor, a resistor, and a capacitor. There is an initial charge of 2 coulombs on the capacitor. At the instant the circuit is closed, a current of 3 amperes is present and a voltage of E(t) = 20 cos t is applied. In this circuit the voltage drop across the resistor is 4 times the instantaneous change in the charge, the voltage drop across the capacitor is 10 times the charge, and the voltage drop across the inductor is 2 times the instantaneous change in the current. Write an initial value problem to model the circuit.arrow_forwardA 100 μF capacitor initially charged to 24 V is discharge across a series combination of a 1 kΩ resistor and a 200 μF capacitor. Find the current after 1 sec.arrow_forwardA 500 ohm resistor, an 1.5 F uncharged capacitor, and a 6.16-V emf are connected in series. (a) What is the initial current? (b) What is the time constant? (c) What is the final voltage on the capacitor? (d) what is the final charge on the capacitor? What is the final energy stored in the capacitor? (e) Express (i) Current in the circuit, (ii) Voltage on the capacitor, (iii) Charge accumulated on either plate of capacitor, (iv) energy stored in the capacitor as a function of time. (must include all the value calculated in the earlier part). (f) What is the i) current ii) charge on capacitor, iii) voltage on capacitor & iv) Energy stored in the capacitor after one time constant?arrow_forward
- A 20-mH inductor and a 18-mH inductor are connected in series with a 3-A current source. Find (a) the equivalent inductance and (b) the total energy stored. (a) mH (b) mJarrow_forward6.2.2 The voltage across a capacitor with 60 UF capacitance has energy function 14. cos“ (a · t) J, where a = 340. Determine the magnitude of the current (in A) through this capacitor when t = 1.3 s. Please pay attention: the numbers may change since they are randomized. Your answer must include 3 places after the decimal point. Your Answer: Answerarrow_forwardCapacitors are fundamental electrical components that store energy in the form of an electric field. They consist of two conductors separated by an insulator, known as a dielectric. When a voltage is applied to the capacitor terminals, it accumulates opposite charges on the conductors, creating an electric field between them. What is the total capacitance (C) in farads (F) between terminals A and B in the capacitor arrangement present in the circuit below?arrow_forward
- A capacitor that is initially uncharged is connected in series with a resistor and a 300.0 V emf source with negligible internal resistance. Just after the circuit is completed, the current through the resistor is 0.950 mA and the time constant for the circuit is 6.00 s. (A) What is the resistance of the resistor? (B) What is the capacitance of the capacitor?arrow_forwardcan you help with 4d this is not and will not be graded 4a. The 6.00 A current through a 1.70 H inductor is dissipated by a 1.50 Ω resistor in a circuit like that in the figure below with the switch in position 2. What is the initial energy in the inductor? 4b. How long will it take the current to decline to 15.00% of its initial value? 4c. Calculate the average power dissipated in the inductor. 4d. What is the ratio of the initial power dissipated by the resistor to the average power dissipated by the inductor.arrow_forwardThe switch in the circuit shown in (Figure 1) has been open for a long time. The initial charge on the capacitor is zero. At t = 0, the switch is closed.arrow_forward
- Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
- Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,