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?

Verified step by step guidance

1. Step 1: Understand the relationship between the components in an RC circuit. In a high-pass RC filter, the input voltage is distributed between the resistor and capacitor. The peak voltage across the resistor and capacitor must add up to the peak voltage of the AC source.
2. Step 2: Use the formula for voltage distribution in the circuit: \( V_{source} = V_{R} + V_{C} \), where \( V_{source} \) is the peak voltage of the AC source, \( V_{R} \) is the peak voltage across the resistor, and \( V_{C} \) is the peak voltage across the capacitor.
3. Step 3: Substitute the given values into the formula. The peak voltage of the AC source is \( 10.0 \, \text{V} \), and the peak voltage across the capacitor is \( 6.0 \, \text{V} \). This gives \( 10.0 = V_{R} + 6.0 \).
4. Step 4: Rearrange the equation to solve for \( V_{R} \), the peak voltage across the resistor. Subtract \( V_{C} \) from \( V_{source} \): \( V_{R} = V_{source} - V_{C} \).
5. Step 5: Substitute the numerical values into the rearranged equation: \( V_{R} = 10.0 - 6.0 \). This will give the peak resistor voltage.

Key Concepts

High-Pass RC Filter

A high-pass RC filter is an electronic circuit that allows signals with a frequency higher than a certain cutoff frequency to pass through while attenuating lower frequencies. It consists of a resistor (R) and a capacitor (C) connected in series, where the output is taken across the resistor. The behavior of the filter is determined by the values of R and C, which set the cutoff frequency.

Voltage Division in RC Circuits

In an RC circuit, the total voltage from the AC source is divided between the resistor and the capacitor. The voltage across each component depends on their impedance and the frequency of the input signal. The relationship can be described using Ohm's law and the concept of reactance, which is the opposition to alternating current due to capacitance or inductance.

Peak Voltage in AC Circuits

The peak voltage in an AC circuit refers to the maximum voltage level reached by the waveform. In this context, the peak voltage of the AC source is given as 10.0 V, while the peak voltage across the capacitor is 6.0 V. The peak voltage across the resistor can be determined by applying Kirchhoff's voltage law, which states that the sum of the voltages in a closed loop must equal zero.