(a)
The current in the inductor as a function of time.
(a)
Answer to Problem 26P
The current in the inductor as a function of time is
Explanation of Solution
Write the expression based on junction rule.
Here,
Write the expression to obtain the loop rule.
Here,
Write the expression to obtain the current in the circuit.
Here, current in the circuit is
The current flow in the circuit is as shown in the figure below.
Figure-(1)
Write the expression to obtain the voltage the loop
Here,
Write the expression to obtain the loop
Here,
Re-write the above equation.
Substitute
Further solve the above equation.
The general solution of the linear differential equation.
Here,
Substitute
Substitute
Substitute
Conclusion:
Substitute
Therefore, the current in the inductor as a function of time is
(b)
The current in the switch as a function of time.
(b)
Answer to Problem 26P
The current in the switch as a function of time is
Explanation of Solution
Consider equation (II) to obtain the current in the switch as a function of time.
Substitute
Further substitute
Conclusion:
Substitute
Therefore, the current in the switch as a function of time is
Want to see more full solutions like this?
Chapter 32 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
- A 5000-pF capacitor is charged to 100 V and then quickly connected to an 80-mH inductor. Determine (a) the maximum energy stored in the magnetic field of the inductor, (b) the peak value of the current, and (c) the frequency of oscillation of the circuit.arrow_forwardConsider the circuit in Figure P32.18, taking = 6.00 V, L = 8.00 mH, and R = 4.00 . (a) What is the inductive time constant of the circuit? (b) Calculate the current in the circuit 250 s after the switch is closed. (c) What is the value of the final steady-state current? (d) After what time interval does the current reach 80.0% of its maximum value?arrow_forwardIn an oscillating LC circuit the maximum charge on the capacitor is 2.0 × 10-6 C and the maximum current through the inductor is 8.0 mA. (a) What is the period of the oscillations? (b) How much time elapses between an instant when the capacitor is uncharged and the next instant when it is fully charged?arrow_forward
- A long, cylindrical solenoid with 100 turns per centimeter has a radius of 1.5 cm. (a) Neglecting end effects, that is the self-inductance per unit length of the solenoid? (b) If the current through the solenoid changes at the rate 5.0 AJs, what is the emf induced per unit length?arrow_forwardA long solenoid with 10 turns per centimeter is placed inside a copper ring such that both objects hove the same central axis. The radius of the ring is 10.0 cm. and the radius of the solenoid is 5.0 cm. (a) What is the emf induced in the ring when the current 2 through the solenoid is 5.0 A and changing at a rate of 100 A/s? (b) What is the emf induced in the ring when 1=2.0A and. dI/dt=100A/s ? (c) What is the electric field inside the ring for these two cases? id: Suppose the ring is moved so that its central axis and the central axis of the solenoid are still parallel but no longer coincide. (You should assume that the solenoid is still inside die ring.) New what is the emf induced in the ring? (el Can you calculate the electric field in die ring as you did in part (c)?arrow_forwardFigure P23.58 is a graph of the induced emf versus time for a coil of N turns rotating with angular speed ω in a uniform magnetic field directed perpendicular to the coil’s axis of rotation. What If? Copy this sketch (on a larger scale) and on the same set of axes show the graph of emf versus t (a) if the number of turns in the coil is doubled, (b) if instead the angular speed is doubled, and (c) if the angular speed is doubled while the number of turns in the coil is halved. Figure P23.58arrow_forward
- A 10.00 μF capacitor C is initially charged to a voltage V of 10.00 (V). It is then connected in series with an inductor L. Charge and current oscillations ensue. (a) What is the total energy U of the circuit? (b) If the maximum current in the inductor is Im = 0.500 (A), then what is the inductance L? What is the charge Q on the positive plate of the capacitor when the current reaches its maximum value Im? (c) What is the angular frequency of the charge oscillations?arrow_forwardc) The current follows in a charging inductor I(t) at time t seconds is given by: i(t) = I,(1 – e7) mA Where I, is the supply current and t= 30. 1. Evaluate the following The current flows in the inductor up to 3 significant figures after 24 seconds if the supply current I, = 75 mA The time t to 3 significant figures taken for current flows in the inductor to reach 40 mA if the supply current Is remains at 75 mA. i. ii. 2. Find an equation for the energy and evaluate it when L= 10 mH.arrow_forwardc) The current follows in a charging inductor I(t) at time t seconds is given by: i(t) = 1,(1- e i) mA Where I, is the supply current and t= 30. 1. Evaluate the following The current flows in the inductor up to 3 significant figures after 24 seconds if the supply current I, = 75 mA The time t to 3 significant figures taken for current flows in the inductor to reach 40 mA if the supply current Is remains at 75 mA. i. ii. 2. Find an equation for the energy and evaluate it when L= 10 mH. d) The generated voltage of a turbine at timet seconds is given by: v(t) = Vssin(0.4nt +) Where Vs is generator voltage in Volts. Evaluate the following: iii. The voltage of the generator after 2.5 seconds if Vs = 70 V. The voltage at time t = 0 seconds to 3 significant figures The time when the generator first reaches maximum voltage, the period, the frequency, and the time displacement. iv. v. Your answer to this part of the task should be supported by suitably annotated graphical evidence to help…arrow_forward
- In the circuit shown in Fig. , switch S1 has beenclosed for a long enough time so that the current reads a steady 3.50 A.Suddenly, switch S2 is closed and S1 is opened at the same instant.(a) What is the maximum charge that the capacitor will receive?(b) What is the current in the inductor at this time?arrow_forwardA 90.0 mH inductor is connected in a circuit. The current through the inductor is given by the function t²-6¹. Estimate the time at which the emf will reduce to zero.arrow_forwardA 24-V battery is connected in series with a resistor and an inductor, with R = 8.8 N and L = 2.0 H, respectively. (a) Find the energy stored in the inductor when the current reaches its maximum value. %3D (b) Find the energy stored in the inductor one time constant after the switch is closed.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning