Physics

Physics

Problem

A series RLC circuit has R=40 ΩR = 40\,\Omega, L=0.10 HL = 0.10\,\text{H} and C=50 μFC = 50\,\mu\text{F}. If it is connected to a 50 Hz50\,\text{Hz} AC source, the phase angle ϕ\phi (in degrees, rounded to the nearest whole number) is closest to a) +39∘+39^{\circ} b) −19∘-19^{\circ} c) −39∘-39^{\circ} d) +51∘+51^{\circ}
Intuitive explanation

In a series RLC circuit, the phase angle tells you whether current leads or lags the voltage—and it depends on whether the circuit is more "capacitive" or "inductive." You'll compare the inductive reactance XL=2πfLX_L = 2\pi f L and capacitive reactance XC=1/(2πfC)X_C = 1/(2\pi f C) to find the net reactance, then use tan⁡ϕ=(XL−XC)/R\tan \phi = (X_L - X_C)/R to find the angle. The sign of the result tells you the direction of the phase shift.

Intuitive explanation

In a series RLC circuit, the phase angle tells you whether current leads or lags the voltage—and it depends on whether the circuit is more "capacitive" or "inductive." You'll compare the inductive reactance XL=2πfLX_L = 2\pi f L and capacitive reactance XC=1/(2πfC)X_C = 1/(2\pi f C) to find the net reactance, then use tan⁡ϕ=(XL−XC)/R\tan \phi = (X_L - X_C)/R to find the angle. The sign of the result tells you the direction of the phase shift.

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