Consider an LC circuit with L = 15 mH and C = 2500 pF (Fig P22.42). At what freq

Question

Consider an LC circuit with L = 15 mH and C = 2500 pF (Fig P22.42). At what frequency is the reactance of the inductor equal to the reactance of the capacitor? What is the resonant frequency of this circuit? (Figure P22.42). At what frequency is the reactance of the inductor equal to the reactance fo the capacitor? What is the resonant frequency of this circuit? Consider the LC circuit in Problem 42 and Figure P22.42. At t = 0, the current is I = 45 mA and the charge q on the capacitor is zero, What is the energy stored in the inductor at t = 0? At some instant the current will be zero. What is the charge on the capacitor at t_1? Find t_1. (There are many possible values of t_1; find the one closest to t = 0.) Using the value of t_1 from part (c), find the magnitudes of I and q at t = 3t_1.

Explanation / Answer

here,

Que 42 :

Capacitor, C = 2500 uF = 2.5*10^-3 F
inductor, L = 15 mH = 0.015 H

Part a:
reactance of inductor, Xl = 2*pi*f*L ( f isfrequency)
reactnace of capacitor, Xc = 1/(2*pi*f*C)

Xl = Xc
2*pi*f*L = 1/(2*pi*f*C)
f = 1/(2*pi*Sqrt(LC))

Part B:
f = 1/( 2*pi*Sqrt(0.015*2.5*10^-3) )
f = 25.99 Hz or 30 Hz( Rounded off)

Ques 43.

at t = 0 , I = 45 mA = 0.045 A

Part A:
Energy, El = 0.5 * L*I^2 = 0.5*0.015*0.045^2
El = 1.519*10^-5 J

Part B:
at time t1,

Energy of inductor = Energy of Capacitor

0.5*L*I^2 = 0.5 * Q^2 / C

El = 0.5 * Q^2/C

Solving for Charge, Q

Q = sqrt(2*El/C)
Q = sqrt(2*1.519*10^-5 / (2.5*10^-3))
Q = 11 C

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---