Capacitors in AC Circuits Practice Problems

Consider a low-pass RC filter circuit consisting of a resistor with a resistance of 200 Ω is connected in series with a capacitance of 50.0 μF. Calculate the crossover frequency (f_C).

In a phase-shift network circuit, a resistor is connected in series with a capacitor. The circuit is powered by an AC source with a peak voltage of 8.0 V. The measured peak voltage across the capacitor is found to be 4.5 V. What is the magnitude of the peak voltage across the resistor in this circuit?

What values do V_r and V_c have when the frequency of the emf for the circuit shown in the figure is 3.5 kHz?

When the angular frequency of the emf in the circuit depicted in the figure shown below is 2.26 × 10³ rad/s, what are the values of the voltage across the resistor (V_r) and the capacitor (V_c)?

Determine an expression for the frequency of an RC series circuit at which V_r = (1/3)ε₀ where ε₀ is the peak value of the input voltage.

Calculate the voltage across the capacitor of an RC series circuit at which V _R equals (1/5)ε₀ where ε₀ is the peak value of the input voltage.

Audio equalizers often incorporate series RC circuits. The circuit components include a 10 kΩ resistor and a parallel-plate capacitor with a radius of 6.5 cm. During a performance test, a 15 V signal at a frequency of 30 kHz is applied, resulting in a peak current of 0.40 mA. Determine the distance between the plates of the capacitor.

The breaking system of an electronic toy car consists of a resistor and a capacitor. This configuration is designed so that the voltage decays to a quarter of its initial value within 3.5 ms to ensure a safe stop. In a subsequent design phase, the same resistor and capacitor are utilized in crafting a low-pass filter for the car's speaker system. This is done to reduce high-frequency distortion and enhance overall sound quality. What would be the crossover frequency (f_c) for this filter?

In high-performance electric motorcycles, the internal power supplies operate at 24.0 V rms, 80 Hz. Design a circuit using a 100 μF capacitor and resistors that generates a 12.0 V rms output leading the input voltage by 45°.

A medical device uses a 0.20 μF capacitor to generate ultrasonic waves. This capacitor is connected to a 20 V AC supply and operates at a frequency of 200 kHz. What is the peak current flowing through the capacitor?

A signal is passed through a tuning capacitor in a radio transmission system. The capacitor handles a peak current of 6.0 mA at a particular broadcast frequency. What would be the peak current if the broadcast frequency tripled, keeping the capacitance fixed?

In a high-frequency generator experiment, a specific capacitor is subjected to a peak current of 6.0 mA at a certain voltage and frequency. What would be the resultant peak current if the applied peak voltage quadrupled while keeping the frequency and capacitance constant?

A tuning capacitor in a 20 kHz radio receiver experiences a peak current of 55 mA with an rms voltage of 7.0 V. Determine the capacitance (C) of this tuning capacitor.

In a sophisticated audio system, a 15 μF capacitor is connected to an amplifier that generates a peak voltage of 3.0 V. Determine the frequency at which the amplifier needs to operate for the peak current to be 30 mA.

An alternating current source that delivers a peak voltage of 6.0 V is connected to a 25 nF capacitor. Determine the value of the instantaneous voltage across the capacitor at which the current flowing through the capacitor reaches its maximum value.

In a household dimmer switch circuit, a capacitor is subjected to a peak voltage of 120 V and experiences a peak current of 500 μA at a frequency of 60 Hz. What is the value of the capacitance of this capacitor?

A radio tuning capacitor is designed to operate at a frequency of 50. kHz with a peak voltage of 3.2 V, resulting in a peak current of 5.0 × 10 ² μA. If the peak voltage remains constant at 3.2 V, determine the peak current when the frequency is increased to 1.0 × 10² kHz.

Determine the highest magnitude of current delivered by the emf in the figure below:

Calculate the highest magnitude of voltage observed across the capacitor with a capacitance of 4.0 μF in the figure.

The output of an AC power source connected to a capacitor has a frequency of 150 Hz and an rms voltage of 25 V. Determine the phase difference Φ between the current and the emf of the power source. Is the current lagging or leading the emf of the power source?

A series circuit has an inductor L, a capacitor C, and a power source of variable angular frequency ω. At the angular frequency, ω₀, the inductive reactance equals the capacitive reactance. Calculate i) the angular frequency ω₀, and ii) the reactances of the inductor (X_L) and capacitor (X_C) for L= 220.0 mH and C= 8.25 μF.

An alternating current power supply of rms voltage 120.0 V and frequency 80.0 Hz is connected to a parallel plate capacitor. The rms current in the circuit is 200.0 mA. Calculate the capacitance of the parallel plate capacitor.

An inductive coil (L = 300 mH) and a parallel plate capacitor (C = 2.30 μF) are connected in series to a power source of variable frequency. The frequency of the power source is set at 1 kHz. i) Calculate the inductive reactance (X_L) of the inductor and ii) the capacitive reactance (X_C) of the capacitor at this frequency. iii) At what frequency f₀ does the inductive reactance equal the capacitive reactance?

In a domestic cooling system, a 0.40 μF capacitor is incorporated into a motor operating on a 20 V AC power source with a frequency of 110 Hz. What is the peak current flowing through the capacitor?