AC Voltage applied to a capacitor

Depending on the circumstances, alternating currents and voltages vary and change their directions over time. They are commonly used in contemporary electronics and electrical systems, among other things, because of their many advantages. In everyday life, resistances, capacitors, and inductances serve as the building blocks of circuits. Capacitors are devices used in electrical engineering that accumulate charges on their plates and then store them. When capacitance is connected to a voltage source, it is vital to understand the circuit’s behaviour to make educated design choices.

AC Voltage applied to a capacitor 

We can determine the voltage generator generated using v = vmsin(t). A capacitor is an electrical device that stores energy. It is a kind of battery that is used to store power. It is a two-terminal passive electrical component that is used in circuits. 

Capacitance is the technical name for the capacitor’s effect. When a capacitor is connected to a voltage source, it draws current to charge the capacitor. Once charged, the capacitor’s potential between its plates equals the potential between its plates and the battery. The current flowing into the capacitor comes to a stop at this point. The phrase “charging the capacitor” refers to this operation.

AC voltage Capacitor 

If we connect a capacitor to a DC source and observe that it conducts no current, we may assume that the capacitor conducts no current. When we connect a lamp to that circuit, the bulb does not illuminate, suggesting any current flowing through the capacitor. This seems to be because we know that a capacitor’s plates are separated by an insulating substance, preventing electricity from passing between them.

A capacitor is connected across an alternating current voltage. A capacitor and an alternating current voltage V, indicated by the symbol, work in concert to create a potential difference between its terminals that swings sinusoidally in response to the voltage. The potential difference or voltage generated by an alternating current may be stated as follows:

VM denotes the magnitude of the oscillating potential difference while denotes the angular frequency. As seen below in the derivation, Kirchhoff’s loop rule may be used to calculate the current flowing through the resistor due to the current-voltage source.

Derivation

Consider a capacitor of capacitance C is connected across an AC source,

Let v = vmsin ωt ——–(1), 

here v – the source voltage, 

vm – peak voltage , 

ω – angular frequency of AC.

The p.d. across the capacitor at any instant of time is v = q/C

According to Kirchoff’s loop rule, 

vm sin ωt – q/C = 0 

Let ωvmC = im be the amplitude of the current, then i = im cos ωt

Capacitive Reactance : XC : Capacitive reactance is given by = XC = 1/ωC = 1/2πνC = 1/2πfC

The SI unit of XC is the ohm (Ω).

Conclusion

Alternating currents and voltages change direction over time, as we’ve seen. Due to their multiple benefits, they are frequently employed in contemporary products and electrical systems. Resistances, capacitors, and inductance make up the majority of circuits in daily use. Capacitors are devices that collect and store electrical charges on their plates. 

We have also seen that a capacitor is linked to an AC power source. v = vm sin(t) is the equation for voltage from the voltage source. A capacitor is a kind of electrical device that retains energy. It’s a two-terminal passive electrical component. Capacitance is the term for the capacitor’s effect. Capacitors take current from a voltage source in order to charge themselves. It is only after the capacitor is fully charged that the potential at its plates is equal to that of the battery’s. 

If a charged capacitor is connected to a circuit in which the potential on the capacitor plates exceeds the potential on the voltage source, it will short circuit. When this occurs, the capacitor begins to operate as a variable voltage source. Capacitor’s voltage drops when current flows through it, reducing the charge on the plates. This is known as the capacitor being discharged.