The charge q on the capacitor in a simple RLC circuit is governed by the oquation Lq"(t) + Rq'(1) +cat) - E), where L is02 herys5 farndethe inductance, R the resistance, C the capacitance, and E the voltage source. Since the resistance of a resistor incroaseswith temperature, assume that the resistor is heatod so that the resistanco at time t is R(1) = 7+t2. IL=0.2 H, C=5 F,E)=0, q(0) =4 C, and q'(0) = 0 A, find the first four nonzero terms in a power series expansion about t=0 for the chargeon the capacitor.9(0)-4 coulombsR)-7+t olunsgr0)-0 amps(Type an exprossion that includes all terms up to ordor 4.)

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The charge q on the capacitor in a simple RLC circuit is govorned by the oquation Lq" (t) + Rq'(1) + c9) - E), where L is the inductance, R the resistance, C the capacitance, and E the voltage source. Since the resistance of a resistor incroases with temperature, assume that the resistor is heated so that the resistance at time t is R) - 7+ta L 02 H, C-5F, E()m0, q(0) = 4 C, und q'(0) = 0 A, find the first four nonzero terms in a power series expansion about t- 0 for the charge on the capacitor. 02 henrys 5 farnde (0)-4 coulomb R)-7t olena ww 0)-0 amps (Type an expression that includes all terms up to order 4.)

The charge q on the capacitor in a simple RLC circuit is govorned by the oquation Lq" (t) + Rq'(1) + c9) - E), where L is the inductance, R the resistance, C the capacitance, and E the voltage source. Since the resistance of a resistor incroases with temperature, assume that the resistor is heated so that the resistance at time t is R) - 7+ta L 02 H, C-5F, E()m0, q(0) = 4 C, und q'(0) = 0 A, find the first four nonzero terms in a power series expansion about t- 0 for the charge on the capacitor. 02 henrys 5 farnde (0)-4 coulomb R)-7t olena ww 0)-0 amps (Type an expression that includes all terms up to order 4.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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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

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The charge q on the capacitor in a simple RLC circuit is governed by the oquation Lq"(t) + Rq'(1) +cat) - E), where L is
02 herys
5 farnde
the inductance, R the resistance, C the capacitance, and E the voltage source. Since the resistance of a resistor incroases
with temperature, assume that the resistor is heatod so that the resistanco at time t is R(1) = 7+t2. IL=0.2 H, C=5 F,
E)=0, q(0) =4 C, and q'(0) = 0 A, find the first four nonzero terms in a power series expansion about t=0 for the charge
on the capacitor.
9(0)-4 coulombs
R)-7+t oluns
gr0)-0 amps
(Type an exprossion that includes all terms up to ordor 4.)

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