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RCL Circuits Question?
A series circuit contains only a resistor and an inductor. The voltage V of the generator is fixed. If R = 20 ohms and L = 3.2 mH, what is the frequency at which the current is one-fourth its value at zero frequency?
2 Answers
- billrussell42Lv 71 decade agoFavorite Answer
For current to be 1/4, the impedance has to be 4 times or 80Ω
Xc = 1/(2πfC)
Xʟ = 2πfL
Impedance Z = √(R² + X²)
where X = Xʟ – Xc
√(R² + X²) = 4*20 = 80 Ω
√(20² + (2πfL)²) = 80 Ω
400 + (2πfL)² = 6400
(2πfL)² = 6000
2πfL = 77.46
f = 77.46 / (2π0.0032) = 3853 Hz
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- 1 decade ago
Current at zero frequency
I(f=0)=V/20
Current at the frequency
I(f)=v/80
the reactants is
80 (ohms)
X= sqrt (400 +(2pi* f* L)^2)=80
400 +(2pi*f*L)^2=6400
40 *3.2^2 *10^-6 f^2=6000
f^2=15*10^6
f=4000