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Ch 32: AC Circuits
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 32: AC CircuitsProblem 17a
Chapter 32, Problem 17a

A low-pass filter consists of a 100 μF capacitor in series with a 159 Ω resistor. The circuit is driven by an AC source with a peak voltage of 5.00 V. What is the crossover frequency fc?

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1
The crossover frequency (also called the cutoff frequency) for a low-pass RC filter is given by the formula: fc=12πRC. Here, R is the resistance, and C is the capacitance.
Substitute the given values into the formula. The resistance R is 159 Ω, and the capacitance C is 100 μF (which is equivalent to 100 × 10⁻⁶ F).
Write the equation with the substituted values: fc=12π×159×100×10-6.
Simplify the denominator by multiplying the constants: 2π×159×100×10-6. This will give the value of the denominator.
Finally, divide 1 by the result of the denominator to find the crossover frequency fc.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Low-Pass Filter

A low-pass filter is an electronic circuit that allows signals with a frequency lower than a certain cutoff frequency to pass through while attenuating higher frequencies. It typically consists of resistors and capacitors, which work together to determine the filter's frequency response. The cutoff frequency is the point at which the output signal power drops to half of the input signal power.
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Example 1

Crossover Frequency (fc)

The crossover frequency, often denoted as fc, is the frequency at which the output signal power is reduced to half its maximum value, corresponding to a -3 dB point in the frequency response. For a simple RC low-pass filter, fc can be calculated using the formula fc = 1/(2πRC), where R is the resistance and C is the capacitance. This frequency is crucial for understanding how the filter behaves in response to different input frequencies.
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Impedance in AC Circuits

In AC circuits, impedance is the total opposition that a circuit presents to the flow of alternating current, combining both resistance and reactance. The impedance of a capacitor decreases with increasing frequency, affecting the overall behavior of the circuit. Understanding impedance is essential for analyzing how components like resistors and capacitors interact in a low-pass filter, particularly in determining the crossover frequency.
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Related Practice
Textbook Question

A capacitor has a peak current of 330 μA when the peak voltage at 250 kHz is 2.2 V. What is the capacitance?

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Textbook Question

What are VR and VC if the emf frequency in FIGURE EX32.19 is 25 kHz?

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Textbook Question

A high-pass RC filter is connected to an AC source with a peak voltage of 10.0 V. The peak capacitor voltage is 6.0 V. What is the peak resistor voltage?

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Textbook Question

A capacitor has a peak current of 330 μA when the peak voltage at 250 kHz is 2.2 V. If the peak voltage is held constant, what is the peak current at 500 kHz?

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Textbook Question

What are VR and VC if the emf frequency in FIGURE EX32.19 is 2.5 kHz?

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Textbook Question

A high-pass RC filter with a crossover frequency of 1000 Hz uses a 100 Ω resistor. What is the value of the capacitor?

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