Asked by AAA
A series RLC circuit with a resistance of 116.0 Ω has a resonance angular frequency of 5.1 ✕ 105 rad/s. At resonance, the voltages across the resistor and inductor are 60.0 V and 40.0 V, respectively.
(b) At what frequency does the current in the circuit lag the voltage by 45°?
(b) At what frequency does the current in the circuit lag the voltage by 45°?
Answers
Answered by
bobpursley
find current at resonance: 60/116
find Xl at resonance (which also is Xc). From those, find L, and C.
so if we want current lagging, the Xl-Xc has to be the net reactance, and you want 45 deg or Xl-Xc to be equal to R
now, knowing L and C (and R) what w will give that Xl-Xc?
find Xl at resonance (which also is Xc). From those, find L, and C.
so if we want current lagging, the Xl-Xc has to be the net reactance, and you want 45 deg or Xl-Xc to be equal to R
now, knowing L and C (and R) what w will give that Xl-Xc?
Answered by
henry2,
At resonance:
I = V/R = 60/116 = 0.52A.
Xl = Vl/I = 40/0.52 = 77.3 ohms.
Xl = 2pi*F*L = 77.3
6.28*5.1*10^5L = 77.3
L = 2.41*10^-5 h.
At -45 degrees:
Xl = R = 116 ohms.
Xl = 2pi*F*L = 116
6.28*F*2.41*10^-5 = 116
F = 7.65*10^5 rad/s.
I = V/R = 60/116 = 0.52A.
Xl = Vl/I = 40/0.52 = 77.3 ohms.
Xl = 2pi*F*L = 77.3
6.28*5.1*10^5L = 77.3
L = 2.41*10^-5 h.
At -45 degrees:
Xl = R = 116 ohms.
Xl = 2pi*F*L = 116
6.28*F*2.41*10^-5 = 116
F = 7.65*10^5 rad/s.
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