A series RLC circuit is driven by a 1.0-kHz oscillator.The circuit parameters are V_rms = 12 V,L = 5.0 mH,C = 4.0 $\mu$F,and R = 20 $\Omega$.Under these conditions the current A)lags the voltage by 22.8º. B)leads the voltage by 22.8º. C)lags the voltage by 41.6º. D)leads the voltage by 41.6º. E)None of these are correct.

Question

Quizplus · Accepted Answer

The phase angle between the voltage and current in a series RLC circuit is given by:

θ = tan⁻¹((XL-XC)/R)

where XL is the inductive reactance, XC is the capacitive reactance, and R is the resistance.

At a frequency of 1.0 kHz,

XL = 2πfL = 2π(1.0x10³)(5.0x10⁻³) = 31.4 Ω
XC = 1/(2πfC) = 1/(2π(1.0x10³)(4.0x10⁻⁶)) = 39.8 Ω

So,

θ = tan⁻¹((31.4 - 39.8)/20) = tan⁻¹(-0.42) = -22.8º

Since the current lags the voltage in an inductive circuit, the answer is A: lags the voltage by 22.8º.

A Series RLC Circuit Is Driven by a 1 μ\muμ F,and R = 20

A Series RLC Circuit Is Driven by a 1 $\mu$ F,and R = 20