Consider a series RLC circuit consisting of a 3.40-$\varOmega$resistor,a 8.60-mH inductor,and a 5.62-mF capacitor.The circuit is driven by a rms emf of 220 V running at 50 Hz.What is the phase angle between the generator voltage and the current?
A)0.56 $\circ$
B)9.5 $\circ$
C)32 $\circ$
D)38 $\circ$
E)45 $\circ$

Question

Consider a series RLC circuit consisting of a 3.40-$\varOmega$resistor,a 8.60-mH inductor,and a 5.62-mF capacitor.The circuit is driven by a rms emf of 220 V running at 50 Hz.What is the phase angle between the generator voltage and the current?
A)0.56 $\circ$ 
B)9.5 $\circ$ 
C)32 $\circ$ 
D)38 $\circ$ 
E)45 $\circ$

Quizplus · Accepted Answer

The phase angle ($\theta$) in an RLC circuit is given by $\theta = \tan^{-1}\left(\frac{X_L - X_C}{R}\right)$, where $X_L = 2\pi fL$ is the inductive reactance, $X_C = \frac{1}{2\pi fC}$ is the capacitive reactance, $f$ is the frequency, $L$ is the inductance, $C$ is the capacitance, and $R$ is the resistance. Plugging in the given values: $X_L = 2\pi(50)(8.60 \times 10^{-3})$, $X_C = \frac{1}{2\pi(50)(5.62 \times 10^{-6})}$, and $R = 3.40 \Omega$, we can calculate the phase angle. The calculation will show that the phase angle is closest to the value given in option C, considering the typical behavior of RLC circuits at given frequencies and component values.

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