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How to Find Voltage Across a Capacitor in an AC Circuit?

Published in Electronics 3 mins read

The voltage across a capacitor in an AC circuit can be determined using the following methods:

1. Using Ohm's Law and Capacitive Reactance:

  • Capacitive reactance (Xc) is the opposition offered by a capacitor to the flow of alternating current. It is calculated as:
    • Xc = 1 / (2πfC), where:
      • f is the frequency of the AC signal in Hertz (Hz)
      • C is the capacitance of the capacitor in Farads (F)
  • Ohm's Law states that the voltage across a component is equal to the current flowing through it multiplied by its resistance. In this case, the resistance is the capacitive reactance.
  • Therefore, the voltage across the capacitor (Vc) can be found by:
    • *Vc = I Xc**, where:
      • I is the current flowing through the capacitor in Amperes (A)

2. Using the Voltage Divider Rule:

  • If the capacitor is part of a series circuit with other components, you can apply the Voltage Divider Rule.
  • The voltage across the capacitor is proportional to its reactance compared to the total reactance of the circuit.
  • *Vc = (Xc / (Xc + Xtotal)) Vtotal**, where:
    • Xtotal is the total reactance of the circuit
    • Vtotal is the total voltage applied across the circuit

3. Using a Oscilloscope:

  • An oscilloscope is an instrument that displays the waveform of an electrical signal.
  • By connecting the oscilloscope across the capacitor, you can directly observe the voltage waveform.
  • The peak-to-peak voltage measured on the oscilloscope represents the voltage across the capacitor.

Examples:

  • Example 1: A 10µF capacitor is connected in an AC circuit with a frequency of 50Hz and a current of 2A.
    • Xc = 1 / (2π 50Hz 10µF) ≈ 318.3 ohms
    • Vc = 2A * 318.3 ohms ≈ 636.6 volts
  • Example 2: A capacitor (Xc = 100 ohms) is in series with a resistor (R = 200 ohms) and connected to a 12V AC source.
    • Xtotal = 100 ohms + 200 ohms = 300 ohms
    • Vc = (100 ohms / 300 ohms) * 12V = 4V

Practical Insights:

  • The voltage across a capacitor in an AC circuit is constantly changing, as the current and reactance vary with the frequency.
  • The voltage across a capacitor is usually measured using a digital multimeter in AC mode.
  • It's important to note that the voltage across a capacitor can be dangerous if not handled properly.

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