Multiple Choice
A 300 µF capacitor is connected to an AC source operating at an RMS voltage of 120 V. If the maximum current in the circuit is 1.5 A, what is the oscillation frequency of the AC source?
31. Alternating Current
Capacitors in AC Circuits
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A low-pass RC filter has a resistor in series with a Capacitor. What is the crossover angular frequency?
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Verified step by step guidance1
Understand that the crossover angular frequency, often referred to as the cutoff frequency, for a low-pass RC filter is given by the formula: \( \omega_c = \frac{1}{RC} \), where \( R \) is the resistance and \( C \) is the capacitance.
Identify the given values: the resistance \( R \) is \( 10\,k\Omega \) (which is \( 10,000\,\Omega \)) and the capacitance \( C \) is \( 450\,\mu F \) (which is \( 450 \times 10^{-6}\,F \)).
Substitute the values into the formula: \( \omega_c = \frac{1}{10,000 \times 450 \times 10^{-6}} \).
Calculate the crossover angular frequency \( \omega_c \) in radians per second. Remember that \( \omega_c \) is typically converted to frequency \( f \) in hertz using the relation \( f = \frac{\omega_c}{2\pi} \).
Compare the calculated frequency with the given options to identify the correct answer.
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