6. a. Draw an RLC circuit with a 0.3 n resistor, 0.1 H inductor, and 5 F capacitor connected in series with an EMF E(t). b. Show that the circuit can be modelled by L+R+= E'(t). dt2 c. Given E (t) = 16 cos 2t. Solve the differential equation for the initial conditions %3D i(0) = 0 = 0. %3D

6. a. Draw an RLC circuit with a 0.3 n resistor, 0.1 H inductor, and 5 F capacitor connected in series with an EMF E(t). b. Show that the circuit can be modelled by L+R+= E'(t). dt2 c. Given E (t) = 16 cos 2t. Solve the differential equation for the initial conditions %3D i(0) = 0 = 0. %3D

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter33: Inductors And Ac Circuits

Section: Chapter Questions

Problem 71PQ: Problems 71 and 72 paired. Figure P33.71 shows a series RLC circuit with a 25.0- resistor, a...

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Concept explainers

Voltage Across Inductor

An actor is a passive electrical component that consists of a coil bent in the form of wire which uses electromagnetism to produce electric current through the coil. When the electric current flows through a conductor that is the coil, a magnetic flux is developed around the conductor. This flow of current through the coil creates a magnetic field based on Fleming's Right-hand thumb rule. If there is any decrease in the current passing through the inductor, then the magnetic field will also decrease and energy is released through the generation of electric current. There is also a secondary voltage inducing in the same coil due to the magnetic flux, since it opposes any changes in the electric current flowing through the circuit. An inductor is also called choke, coil, or solenoid. A choke is designed to block certain frequencies when the DC current passes. A winding coil is coated with insulation to give extra insulation and protect the circuit. They are usually tightly wrapped around a central core which is cylindrical in nature so that the magnetic flux can be induced. The solenoid is a three-dimension coil that is used to exhibit electromagnetism when the magnetic field is developed due to the current flowing through the coil. The sign convention of the inductor is the same as the power dissipating device. When the current flows into the positive side of the voltage across the inductor, the value is positive and the inductor dissipates power whereas when the inductor releases the power back to the circuit, the current has a negative sign convention. 

Question

6. a. Draw an RLC circuit with a 0.3 N resistor, 0.1 H inductor, and 5 F capacitor connected in
series with an EMF E(t).
b. Show that the circuit can be modelled by L
+R+= E'(t).
%3D
dt
c. Given E(t)
= 16 cos 2t. Solve the differential equation for the initial conditions
i(0) = i'(0) = 0.
%3D

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