Capacitor Voltage

Capacitor Voltage

  1. Introduction to Capacitor Voltage

A capacitor is an electrical component that stores energy in an electric field. The voltage across a capacitor () is a crucial parameter that determines the amount of charge stored and the energy stored in the capacitor.

  1. Relationship between Charge and Voltage

The charge () stored on a capacitor is directly proportional to the voltage across it. The relationship is given by the formula , where  is the capacitance of the capacitor. Capacitance is a measure of the capacitor's ability to store charge and is measured in farads (F). For example, if a capacitor has a capacitance of  (microfarad, ) and a voltage of  across it, the charge stored is  (coulombs).

  1. Charging and Discharging of a Capacitor

  • Charging Process: When a capacitor is connected to a DC voltage source through a resistor (in a series RC circuit), the capacitor starts to charge. Initially, the voltage across the capacitor is zero. As time passes, the charge on the capacitor builds up, and the voltage across it increases. The voltage across the capacitor during charging is given by the formula , where  is the source voltage,  is the time,  is the resistance in the circuit, and  is the capacitance. The product  is called the time constant () of the circuit. For example, if , , and , the time constant . After a time equal to about  (in this case, ), the capacitor is almost fully charged, and the voltage across it is approximately equal to the source voltage.
  • Discharging Process: When a charged capacitor is disconnected from the voltage source and connected across a resistor, it starts to discharge. The voltage across the capacitor during discharging is given by the formula , where  is the initial voltage across the capacitor when discharging begins. The voltage across the capacitor decreases exponentially with time.

  1. Capacitor Voltage in AC Circuits

In an AC circuit, the voltage across a capacitor varies sinusoidally. The capacitive reactance () is a measure of the opposition offered by the capacitor to the flow of AC current. It is given by the formula , where  is the frequency of the AC signal. The voltage across the capacitor in an AC circuit is related to the current () through the capacitor by the formula . For example, if the current through a capacitor is , the capacitance is , and the frequency of the AC signal is , the capacitive reactance , and the voltage across the capacitor .

  1. Applications Related to Capacitor Voltage

  • Power Supply Filtering: Capacitors are used in power supplies to filter out the ripple voltage. In a rectifier circuit, the output of the rectifier contains a pulsating DC voltage. By connecting a large - value capacitor in parallel with the load, the capacitor charges during the peaks of the pulsating voltage and discharges during the troughs, smoothing out the voltage and providing a more stable DC output. The voltage across the capacitor remains relatively constant, reducing the ripple factor.
  • Timing Circuits: In RC timing circuits, the voltage across the capacitor is used to trigger other components at a specific time. For example, in a 555 timer circuit configured as a monostable multivibrator, the charging of a capacitor determines the time period for which the output pulse is high. The voltage across the capacitor is compared with a reference voltage to trigger the change in the output state of the timer.