, Damped oscillations, and Faraday: An RLC series cirenit is poweredbr a sinusoidal voltage source V,(t) = |Vo]cos wt.) Assume a direction for the current and show it on your figure. Considerthe clased loop line integral of the electric ficld along the current directionassumed, and obtain the equation for charge q on the capacitor.) For times much later than the damping time (t >> Tu = (R/L)-'), com-pute the correlation function < Vc»(t) Vcp(t + A) > where Vc,(t) is thevoltage across the capacitor.(Hint: If A, = Re.A.c"t and Bp = Rc.B,e*, then < A,B, >=ĮRe.A;B,, and VcpŻL = iwL and ZR = R).Re.A,B; =-i. Also%3DRe.Vc with Vc = İZc and Zc =%3D%3DR\vol coswt

Impedance of the circuit, Z=R+jXL-XC

1 Damped oscillations, and Faraday: An RLC series cirenit is powered br a sinusoidal voltage source V,(t) = |Volcos wt. ) Assume a direction for the current and show it on your figure. Consider the closed loop line integral of the electric ficll along the current direction Asumed, and obtain the equation for charge q on the capacitor. b) For times much later than the damping time (t >> Tu = (R/L)-'), com- pute the correlation function < Vc»(t) Vcp(t + A) > where Ve»(t) is the voltage across the capacitor. (Hint: If A, = Re.A.cut and B, = Re.B,et, then < A„B, >= ĮRe.A;B,, and Vcp Ż2 = iwL and ZR = R). %3D %3D Re.A,B; = -i. Also %3D %3D Re.Vc with Vc ize and Zc = %3D %3D %3D R lvolcoscwt cl

1 Damped oscillations, and Faraday: An RLC series cirenit is powered br a sinusoidal voltage source V,(t) = |Volcos wt. ) Assume a direction for the current and show it on your figure. Consider the closed loop line integral of the electric ficll along the current direction Asumed, and obtain the equation for charge q on the capacitor. b) For times much later than the damping time (t >> Tu = (R/L)-'), com- pute the correlation function < Vc»(t) Vcp(t + A) > where Ve»(t) is the voltage across the capacitor. (Hint: If A, = Re.A.cut and B, = Re.B,et, then < A„B, >= ĮRe.A;B,, and Vcp Ż2 = iwL and ZR = R). %3D %3D Re.A,B; = -i. Also %3D %3D Re.Vc with Vc ize and Zc = %3D %3D %3D R lvolcoscwt cl

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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