Consider a source that produces varying potential differences across its terminals in sinusoidal form. Let this potential difference, also called AC voltage, be given by , where is the amplitude of the oscillating potential difference and ω is its angular frequency.

To find the value of current through the resistor, apply Kirchhoff’s loop rule  to the circuit to get

As R is a constant, this equation can be written as , where the current amplitude is given by

When plotted on a graph, the values of v and i reach zero, minimum and maximum

values simultaneously, indicating that the voltage and the current are in phase with each other when voltage is applied to a resistor. The current, like the applied voltage, varies sinusoidally and has corresponding maximum and minimum values during each phase. Therefore, the total current over one complete cycle and the average current are both zero.

An inductor, a capacitor, or a combination of the two are not in phase with the AC voltage, unlike in resistors. Phasors are used to indicate the phase relationship between voltage and current in an AC circuit. A phasor diagram is used to analyze an AC circuit. A phasor, which is a rotating vector, rotates about the origin with an angular speed ω. Sinusoidally varying quantities v and i are represented by the vertical components of phasors V and I. The magnitudes of phasors V and I give the amplitudes vm and im of these oscillating quantities respectively. vm sinωt and im sinωt give the instantaneous values of voltage and current respectively. Curves are generated as they rotate with frequency ω. In the case of a resistor, phasors V and I are constantly in the same direction, meaning that the phase angle between the voltage and the current is zero.

When electric current flows through a circuit, an inductor in the circuit is used to store energy in the magnetic field. The inductor can prevent the flow of alternating current through it. The inductor either gains or loses charge. The current across the inductor changes to equalise the current passing through it. The voltage in an inductor is calculated by the amount of electromotive force (EMF) that is required to bring about the change in current. For example, if an inductor produces an EMF of 1V when current passes through it, the inductor has an inductance value of 1 Henry and changes at the rate of 1 ampere per second.

The current phasor I is π/2 behind the voltage phasor V. When rotated at a frequency ω, the voltage and current is given by:

 and .

This section of the NCERT Solutions for Class 12 Chapter 7 Physics explains what happens when AC voltage is applied to an inductor and how the current is behind the voltage by a phase difference of π/2.

When a voltage source is applied to a capacitor in a DC circuit, the current flows until the capacitor is charged. As charge increases in the capacitor plates, voltage across them increases as well and opposes the current, meaning a capacitor in a DC circuit limits the current as it charges. When the capacitor is charged completely, the current in the circuit falls right down to zero. When an AC voltage is supplied to the capacitor, the flow of current is limited but not completely prevented by the capacitor. The capacitor is charged and discharged alternately as the current reverses each half cycle. This section of the NCERT Solutions for Class 12 Chapter 7 Physics explains what happens when AC voltage is applied to a capacitor and how the angle of the phase difference between the current and voltage is π/2, with the current leading the voltage.

An LCR circuit is a circuit consisting of an inductor, a capacitor and a resistor connected in series or parallel. This section explains what happens when AC voltage is applied to a series LCR circuit, and how the equation for the current in the LCR circuit is derived.

If θ = 0, then the voltage and the current in the LCR circuit are in phase. If θ = π/2, then the voltage and the current in the LCR circuit are out of phase.

While capacitors store electrical energy, inductors store magnetic energy. When a charged capacitor C is connected to an inductor L, then the charge on the capacitor and the current in the circuit go through electrical oscillations, which is similar to oscillations in mechanical systems. These oscillations between the capacitor and inductor are referred to as LC oscillations.

The capacitor starts charging when an AC voltage is applied in the circuit. At full charge, the capacitor starts discharging while the charge is transferred to the inductor connected to the capacitor. Due to the change in the current, the magnetic flux of the inductor in the circuit also changes, resulting in an emf induced in the inductor. This emf in the inductor opposes the rise in the current, because of which when the capacitor is completely discharged, all the energy stored in the capacitor is stored in the inductor. Then the inductor starts charging the capacitor. The energy stored in the capacitor starts to rise again. This cycle repeats, creating LC oscillations.

A transformer is a device that is used to add or reduce the voltage in a circuit without changing the frequency of the alternating current in the circuit. A transformer is made up of two sets of insulated coils, each with a different number of turns wound on a soft-iron core. One of the coils is the primary coil while the other is the secondary coil. Generally, the input coil is the primary coil and the output coil is the secondary coil. The power entering the transformer at the input coil is equal to the power exiting at the output end. Transformers work on the principle of electromagnetic and mutual induction and are used in various fields such as a power grid, manufacturing processes, circuit breakers, and more.

1 . What is alternating current?

Alternating current (AC) is the current whose magnitude and direction vary periodically.

2 . How to measure alternating current?

Alternating current can be measured using ammeters, tong testers or clamp meters. It can also be calculated by dividing the peak voltage by the resistance in a circuit.

3 . Why does alternating current change its direction?

In an alternator, when a loop of wire is spun inside a magnetic field, an electric current is generated along the wire. As the wire spins and periodically changes its magnetic polarity, the voltage and current also change along the wire. This current changes direction at particular intervals of time, which in turn changes the voltage.