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Alternating Current

Alternating Current :- So far in the previous chapters we have studied direct current circuits in which a cell or battery was used as the source of emf and the current I was controlled by a single ohmic resistance R according to Ohm’s law (V = IR). In such circuits, the magnitude and direction of electric current remain constant with time, hence it is called direct current.

However, the mains electric supply found in our homes and offices is a source of voltage that varies with time as a sine function. This type of voltage is called alternating voltage (AC Voltage) and the current flowing through it in an electric circuit is called alternating current (AC Current).

Nowadays, electrical energy is generally produced and used in the form of alternating current. There are two main reasons for this :

The magnitude of the alternating voltage can be easily changed using a transformer, and
Alternating electrical energy can be easily transmitted to distant places with minimal energy loss.

(1) Direct Current and voltage

The electric current/voltage whose magnitude and direction do not change with time is called direct current/voltage.

Graph between direct current/voltage and time :-

In figure (a) the magnitude of direct current is constant and in figure (b) and (c) uneven direct current is shown.

Non-uniform direct current :- A current whose direction remains unchanged over time but whose magnitude varies is called non-uniform direct current. It is also called Pulsating Direct Current (Pulsating DC).

Note :-

The source of direct current is a battery or cell.
The frequency of direct current/voltage is zero (f = 0) and the time period is infinite [T = (1/f ) = ∞].
Direct current is measured by an ammeter based on the principle of a moving coil galvanometer.

(2) Alternating Current and voltage

A voltage or electric current whose magnitude and direction change periodically with time is called alternating current or alternating voltage. It can be represented by a sine or cosine curve.

Amplitude of AC

The maximum value of the current in one direction (positive or negative) is called the amplitude. It is represented by I₀.
peak to peak value = 2I₀

Time Period/Periodic Time
The time taken by alternating current to complete one cycle of change is called the time period of alternating current.

Frequency
The number of cycles completed by alternating current in one second is called frequency. Frequency is represented by ν (nu).

Unit – cycle/second or hertz (Hz)

Electricity supply to homes in India: Frequency = 50 Hz, Voltage = 220 V

Electricity supply to homes in America: Frequency = 60 Hz, Voltage = 110 V

The magnitude of an alternating quantity becomes zero twice and reaches its maximum value twice in each complete cycle. Therefore, in one second, it becomes zero 2ν times and attains maximum value 2ν times, where ν is the frequency of the AC. Additionally, the direction of the alternating quantity reverses 2ν times per second.

In AC circuits, two additional components, inductor (L) and capacitor (C) are used along with resistance (R), hence in AC circuits, the current is controlled by three components R, L and C.

The potential difference V across a pure inductor L,

$\displaystyle V=L\frac{dI}{dt}$ …..(1)

Where $\displaystyle \frac{dI}{dt}$ is the rate of change of electric current I.

Similarly, for an ideal capacitor C,

$\displaystyle Q=CV$

Hence, the current I flowing through the capacitor,

$\displaystyle I=\frac{dQ}{dt}=\frac{d}{dt}(CV)$

$\displaystyle \Rightarrow I=C\frac{dV}{dt}$ …..(2)

Where $\displaystyle \frac{dV}{dt}$ is the rate of change of electric potential V.

According to equation (1), an inductor affects the potential difference when the current I changes and according to equation (2), a capacitor affects the current when the potential difference V changes with time. Hence, in AC circuits, V and I depend on time.

Transient Current

If an electric circuit consisting of only resistance R is switched on or off, the electric current attains its maximum value immediately. But if an inductor L or a capacitor C is connected in the circuit, then due to the induced emf, the current takes some time to reach its maximum value and decay.

Therefore, a transient current is defined as the temporary current that arises in a circuit due to the opposition of an inductor to the change in current over time, or due to the opposition of a capacitor to the change in voltage, and this current diminishes over time as the circuit reaches its steady state.

Next Topic :- Rise and Decay of Current In Inductive Circuit

Complete List of Topics :-

Alternating Current

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