Consider a series RLC circuit where R = 855 Ohm. C = 7.25 mu F and L = 95.0 mH.
ID: 1425987 • Letter: C
Question
Consider a series RLC circuit where R = 855 Ohm. C = 7.25 mu F and L = 95.0 mH. Determine the resonance frequency at, of the circuit (Recall that w-2rrf) What is the maximum current when the circuit is at resonance, if the amplitude of the (ac) voltage is 24.0 V? A series RL circuit includes a 3.05-V battery, a resistance R = 0.455Ohm, and an inductance of L - 3.23 H. What is the induced emf 1.33 s after the circuit has been closed? Consider a series RLC circuit where R = 345 Ohm and C = 1.25 mu F. However, the inductance L of the inductor is unknown. To find its value, you decide to perform some simple measurements. You apply an ac voltage that peaks at 84.0 V and observe, using an oscilloscope, that the resonance angular frequency occurs at 27500 s^-1 (recall that omega = 2 pi f). What is the inductance of the inductor in mill henrys?Explanation / Answer
RLC circuit resonace frequency W_0 = 1/sqrt(LC)
W_0 = 1/sqrt(95*10^-3*7.25*10^-6)= 1204.95 Hz
Maximum current when the circuit is at resonance is I = V/R = 24/855 = 0.02807 A = 28.07 mA
in series RL circuit
the current at t = 1.33s is
i(t) = I[1-e^-t/(L/R)]
= (3.05/0.455)[1-e^-1.33/(3.23/0.455)]
= 1.1452 A
now emf at t= 1.33 s is v = i(1.33)*0.455= 1.1452*0.455 = 0.521 V
resonance frequency in RLC circuit is W_0 = 1/sqrt(LC)
given W_0 = 27500 s-1
L = 1/ W_0^2*C
= 1/(27500^2*1.25*10^-6)
= 1.058 mH