Many electrical circuits feature resistors, inductors, and capacitors connected across an AC source and combine any two or all three of these components connected across an AC source. When a resistor is used, the current flowing through it is in phase with the voltage source. An AC power source’s output is sinusoidal and fluctuates with time according to the equation: v(t) = V0sin(ωt) The instantaneous voltage is v(t). V0 is the maximum output voltage of the source, which is known as the voltage amplitude ( Vmax).

## How Is AC Voltage Generated

Faraday’s Law of Induction allows AC voltage to be produced. The law explains how electric currents can be created in a moving coil by cutting through magnetic flux at an angle. The rate of change in magnetic flux is proportional to the current change.

Faraday’s Law is used to construct AC alternators and generators. A loop of conductors is rotated over a magnetic field in these experiments. The current starts to flow in one direction when the loop cuts through the magnetic field, and it reaches its maximum when the loop is perpendicular to the magnetic field.

The loop rotates indefinitely until the conductor is parallel to the magnetic flux, resulting in zero current. As the loop begins to cut the magnetic flux in the opposite direction, the current flows in the opposite direction.

## AC voltage applies to a resistance:

A circuit consists of AC sinusoidal voltage source and resistance denoted by R. When the voltage and current flowing through it are in phase, Resistance R resists the electric flow through the circuit.

Here is the method of finding the resistance based on the equation:

The following is the equation for the voltage applied to the resistance of a pure resistance circuit:

v = Vmsin ωt

On application of the voltage, it will lead to the flow of the alternating current in the circuit represented by i.

Hence, the total voltage applied across the resistance is shown by:

v = iR

i = v/R = Vmsin ωt/R = Imsin ωt

Im = Vm /R, which represents the maximum value of the circuit

## Ac voltage applied to a capacitor

There is a capacitor linked to a DC source; however, no current runs through it. In case the lamp is attached to the circuit, the lamp will not light, indicating that no current flows through the capacitor. This makes sense because we know there is an insulating material between the plates of a capacitor, which prevents electricity from flowing through it.

In case an AC source is connected to the capacitor, the current starts to flow through it, and in case the lamp is plugged, the lamp shines, indicating that current is flowing through the AC circuit. In a DC circuit, a capacitor is an insulator, but in an AC circuit, it is a conductor.

The current is created by connecting a steady power source or a battery to a resistor. The created current travels in a single direction and has a constant magnitude. In general, current travels from the battery’s negative to positive terminals. An alternating current is one in which the current direction fluctuates alternately across the resistor. This handout discusses some of the RLC series circuit difficulties and their remedies.

An electric circuit containing a constant voltage source, a resistor, and the key-current is formed the time the key is inserted. Any current travelling in a circuit has a specific direction, from the battery’s negative terminal to the positive terminal. According to Ohm’s law (V = IR), if the voltage’s magnitude and the resistance remain constant, the circuit’s current will also remain constant.

However, an alternating voltage source can be used instead of the battery across the entire resistor. As a result, the current direction around the resistor will alternate, and the current is known as Alternating Current. The AC generator, also called the AC dynamo, can be used to generate alternating voltage.

## AC voltage applied to a inductor:

With the AC circuit containing inductance only, as only the inductor is present, it reserves the electrical energy and converts it into a magnetic field with the current flow through it. As the direction of current or voltage changes, the impact of the time-varying magnetic field leads to the electromotive force opposing the current flow.

Hence, it is known to control the current flow’s fluctuation, and opposition is called inductive reactance.

The equation of the AC circuit containing inductance only meaning proves that the current in the pure inductive AC circuits lags the voltage by 90°.

Let the voltage in the circuit be

v = VmSin ωt

The electromotive force (EMF) in the inductor is

E = – L x dl/dt

In comparison, the EMF induced in the circuit is equal and opposite to the voltage applied.

Hence, we can imply that v = E

v = – L x dl/dt

Putting the value of v

VmSin ωt = – L x dl/dt

On integrating the sides, we can conclude that in the case of the pure inductive AC circuits, it lags the voltage by 90°.

## What is an LCR Circuit?

The LCR circuit is commonly referred to as a tuned or resonant circuit. It’s an electrical circuit made up of an inductor (L), a capacitor (C), and a resistor (R). The resistor, inductor, and capacitor are linked in series in this circuit, resulting in the same amount of current flowing through it. In general, the differential equation of an RLC circuit is comparable to that of a forced, damped oscillator. Some terms, such as impedance, are used to derive the LCR circuit equations. The resistance in the LCR series circuit is referred to as impedance. The resistance provided by the inductor, resistor, and capacitor is all included.

### Conclusion

Since AC and voltage are sinusoidal, phasors are often not used to represent them. The current is created by connecting a steady power source or a battery to a resistor. The created current travels in a single direction and has a constant magnitude. In general, current travels from the battery’s negative to positive terminals. Alternating current is the electric current where the direction of the current electricity keeps on changing.