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Studying Physics Topics can lead to exciting new discoveries and technological advancements.

## What is Electric Current: The Basics

When two charged bodies at different electric potentials are connected by a metal wire, then electric charges will flow from the body at higher potential to the one at lower potential (till they both acquire the same potential). This flow of charges in the metal wire constitutes an electric current. It is the potential difference between the ends of the wire which makes the electric charges (or current) to flow in the wire. We now know that the electric charges whose flow in a metal wire constitutes electric current are the negative charges called electrons. Keeping this in mind, we can now define electric current as follows,

The electric current is a flow of electric charges (called electrons) in a conductor such as a metal wire. The magnitude of electric current in a conductor is the amount of electric charge passing through a given point of the conductor in one second. If a charge of Q coulombs flows through a conductor in time t seconds, then the magnitude I of the electric current flowing through it is given by :

Current, I = \(\frac{Q}{t}\)

The SI unit of electric current is ampere which is denoted by the letter A. We can use the above formula to obtain the definition of the unit of current called ‘ampere’. If we put charge Q = 1 coulomb and time t = 1 second in the above formula, then current I becomes 1 ampere. This gives us the following definition of ampere : When 1 coulomb of charge flows through any cross-section of a conductor in 1 second, the electric current flowing through it is said to be 1 ampere. That is,

1 ampere = \(\frac{1 \text { coulomb }}{1 \text { second }}\)

or 1 A = \(\frac{1 \mathrm{C}}{1 \mathrm{~s}}\)

Sometimes, however, a smaller unit of current called “milliampere” is also used, which is denoted by mA.

1 milliampere = \(\frac{1}{1000}\) ampere

or 1 mA = \(\frac{1}{1000}\) A

or 1 mA = 10^{-3} A

Thus, the small quantities of current are expressed in the unit of milliampere, mA (1 mA = 10^{-3} A). The very small quantities of current are expressed in a still smaller unit of current called microampere, pA (1 µA = 10^{-6} A).

Current is measured by an instrument called ammeter (see Figure). The ammeter is always connected in series with the circuit in which the current is to be measured. For example, if we want to find out the current flowing through a conductor BC (such as a resistance wire), then we should connect the ammeter A in series with the conductor BC as shown in Figure. Since the entire current passes through the ammeter, therefore, an ammeter should have very low resistance so that it may not change the value of the current flowing in the circuit. Let us solve one problem now.

**Example Problem.**

An electric bulb draws a current of 0.25 A for 20 minutes. Calculate the amount of electric charge that flows through the circuit.

**Solution:**

Here, Current, I = 0.25 A

Charge, Q = ? (To be calculated)

And Time, t – 20 minutes

= 20 × 60 seconds

= 1200 s

We know that, I = \(\frac{Q}{t}\)

So, 0.25 = \(\frac{Q}{1200}\)

Q = 0.25 × 1200 C

Q = 300 C

Thus, the amount of electric charge that flows through the circuit is 300 coulombs.

### How to Get a Continuous Flow of Electric Current

We have just studied that it is due to the potential difference between two points that an electric current flows between them.

The simplest way to maintain a potential difference between the two ends of a conductor so as to get a continuous flow of current is to connect the conductor between the terminals of a cell or a battery.

Due to the chemical reactions going on inside the cell or battery, a potential difference is maintained between its terminals.

And this potential difference drives the current in a circuit in which the cell or battery is connected. For example, a single dry cell has a potential difference of 1.5 volts between its two terminals (+ terminal and – terminal). So, when a dry cell is connected to a torch bulb through copper connecting wires, then its potential difference causes the electric current to flow through the copper wires and the bulb, due to which the bulb lights up (see Figure).

In order to maintain current in the external circuit, the cell has to expend the chemical energy which is stored in it. Please note that the torch bulb used in the circuit shown in Figure 8 is actually a kind of ‘conductor’. We can also call it a resistor. It is clear from the above discussion that a common source of ‘potential difference’ or ‘voltage’ is a cell or a battery. It can make the current flow in a circuit.

### Direction of Electric Current

When electricity was invented a long time back, it was known that there are two types of charges: positive charges and negative charges, but the electron had not been discovered at that time. So, electric current was considered to be a flow of positive charges and the direction of flow of the positive charges was taken to be the direction of electric current.

Thus, the conventional direction of electric current is from positive terminal of a cell (or battery) to the negative terminal, through the outer circuit. So, in our circuit diagrams, we put the arrows on the connecting wires pointing from the positive terminal of the cell towards the negative terminal of the cell, to show the direction of conventional current (see Figure 8). The actual flow of electrons (which constitute the current) ‘is, however, from negative terminal to positive terminal of a cell, which is opposite to the direction of conventional current.

### How the Current Flows in a Wire

We know that electric current is a flow of electrons in a metal wire (or conductor) when a cell or battery is applied across its ends. A metal wire has plenty of free electrons in it.

(i) When the metal wire has not been connected to a source of electricity like a cell or a battery, then the electrons present in it move at random in all the directions between the atoms of the metal wire as shown in Figure.

(ii) When a source of electricity like a cell or a battery is connected between the ends of the metal wire, then an electric force acts on the electrons present in the wire. Since the electrons are negatively charged, they start moving from negative end to the positive end of the wire (see Figure).

This flow of electrons constitutes the electric current in the wire.

### Introduction

An electric current is a flow of charges—which is often carried by electrons through a wire. It can also be carried by ions. Elec-tric current is a physical quantity which can be measured and expressed numerically. The principal function of any source of electricity is to send current in an external circuit.

In this chapter we shall discuss about the electric current follow-ing Ohm’s law.

Electric current can be compared with flow of water or flow of heat. If there is a difference in the level of water in two vessels connected by a pipe, water moves from the higher level to the lower one. Similarly, if there is a difference in temperature between two bodies connected by a thermal conductor, heat flows from the body having higher temperature to the body hav-ing lower temperature.

Similarly, if there is a potential difference between two charged bodies and if they are connected by an electrical conductor, positive charge moves from the body at higher potential to the body at lower potential until equilibrium is reached.

The two vessels A and B are connected by a pipe C [Fig. (a)]. If there is a difference in water levels in the two vessels, water flows through the pipe C. In Fig.(b) the two bodies A and B are connected by the rod C. If there is any difference in temperature between the two bodies, heat flows through the rod C, until the temperature difference is reduced to zero.

Similarly, two charged bodies A and B are connected by a con-ducting wire C [Fig.(c)]. If there is a difference of potential between the two bodies, electric charge flows through the con-necting wire C, until a common potential is attained.

Definition: Flow of electric charge through a conductor is called electric current.

Current strength or simply current in a conductor is defined as the net flow of charge in unit time through any cross section of the conductor.

Therefore, current (I) \(=\frac{\text { charge }(Q)}{\operatorname{time}(t)}\)

∴ I = \(\frac{Q}{t}\) or, Q = It

When the rate of flow of charges through any cross section of a conductor is not uniform then current varies with time.

In this case, current will be a function of time, i.e., I = f(t). The instantaneous current (i) is defined as,

i = \(\frac{d Q}{d t}\)

We can find the net charge that passes through a cross section in a time interval extending from 0 to t, by integration. Thus,

Q = \(\int d Q\) = \(\int_0^t i d t\)

Unit of electric Current: According to the above definition of current,

unit of current \(=\frac{\text { unit of charge }}{\text { unit of time }}\)

i.e., 1 ampere \(=\frac{1 \text { coulomb }}{1 \text { second }}\)

or, coulomb = ampere × second

So, the current flowing through a conductor is said to be 1 ampere (A) if 1 coulomb (C) of charge flows through its cross section in 1 second (s).

### Numerical Examples

**Example 1.**

Current I flows through a wire depends on time t as follows: I = 3t^{2} + 2t + 5. How much charge flows through the cross section of the wire from t = 0 to t = 2s?

Solution:

The charge flowing through the cross section of the wire is

**Example 2.**

If a current I = 4πsinπt ampere flows through a wire, then find the amount of charge that flows through the wire in

(i) t = 0 to t = 1s and

(ii) t = 1s to t = 2s.

Solution:

i) In this case, t_{1} = 0 and t_{2} = 1s

Therefore, Q_{1} = 4(cos0 – cosπ) = 4[1-(-1)] = 8 C

ii)In this case, t_{1} = 1s and t_{2} = 2s

Therefore, Q_{2} = 4(cosπ – cos2π) = 4(-1 – 1) = -8C

Here the current I = 4πsinπt denotes an alternating current (see chapter ‘Alternating Current’ for details). Its time period is 2 seconds. The above example indicates that in the first half cycle i.e., in first 1 second, the amount of charge flowing through any cross section is equal to the charge flowing in the second half cycle i.e., in next 1 second but in opposite direction. So, that net charge flowing through any particular cross section inside a conductor in a total cycle is zero. It is a property of an ac.

### Conventional Direction of Electric Current

Of two bodies, the body at a higher potential is called a positively charged body and the body at a lower potential is called a negatively charged body. Similar is the case for two points on a conductor.

Now, from the properties of electric potential we know that (See Chapter ‘Electric Potential’]

1. if free positive charges exist in a conductor, they flow from the higher to the lower potential and

2. if free negative charges exist in a conductor, they flow from the lower to the higher potential i.e., the directions of flow of positive and negative charges are opposite to each other. We take, the direction of flow of free positive charge as the direction of flow of electric current i.e., conventionally, the direction of flow of current is from higher potential to lower potential (Fig.).

It is to be noted that water flows from a higher level to a lower level. Similarly heat flows from higher temperature to a Lower temperature. So conventional direction of current from higher potential to lower potential is analogous to flow of water or flow of heat.

In a metallic conductor current flows due to the movement of free electrons. Since the electrons are negatively charged, they flow from lower potential to higher potential. So this direction is obviously opposite to the conventional direction of current[Fig.].

Direct current or dc: If a current flows continuously in the same direction through a conductor, it is called direct current or dc.

Alternating current or ac: If a current flowing through a conductor periodically reverses its direction, it is called alternating current or ac.

### Source of Electric Current

Flow of water and electric current are two similar phenomena [Fig.(a) and (b)]. From the Fig.(a) it is easily understood that flow of water through the pipe C will not continue for a long period because the levels of water in the vessels A and B will become equal within a short time. But if the difference of water level is maintained with the help of the pump P by sending water continuously from the vessel B to the vessel A, water will continue to flow through the pipe C. It is to be noted that cooperate the pump P energy must be supplied by an external source. This external acts as the source of flow of water in the pipe C.

Similarly to get continuous flow of current in the conductor C by maintaining Constant potential difference between the bodies A and B, an arrangement similar to the pump P is required [Fig. (b)]. This arrangement continuously sends positive charges from the body B to the body A. To do this work the arrangement takes the help of some external SOUCC of energy.

As a result, a constant potential difference is maintained between the two bodies. So this arrangement P is the source of continuous flow of current in the conducting wire C. This is called source of electricity in short.

On observing the Fig. (b) and considering the similarity between flow of water and electric current some relevant informations are obtained—

i) Electric circuit: The path ACBPA is a continuous path i.e., there is no break in the path of flow of free charges. This type of a continuous path is called an electric circuit.

ii) Closed circuit and open circuit: By using a stopcock in a pipe through which water flows we can maintain the flow or stop it according to our will. Similarly by using a switch in an electrical circuit, current may be allowed to flow or it may be stopped. If the switch is on, there is no break in the circuit. This is called a closed circuit. Again if the switch is off, the circuit becomes discontinuous. It is called an open circuit. Current does not flow in an open circuit.

iii) Uniformity of electric current: Obviously the rate of flow of free charges through every point of a closed circuit is the same i.e., current flows uniformly in every part of a closed circuit. It follows an important principle which states that charges do not accumulate at any point in a conductor carrying a current. In other words, there is no source or sink for electric charges in a conductor.

iv) Internal circuit: In the part BPA of the circuit, any form of external energy is converted to electrical energy. This part of the circuit is included in the source of electricity and is called the Internal circuit.

v) External circuit: In the part ACB of the circuit, electrical energy is converted to any other form of energy; e.g., by lighting an electric lamp, heat energy and light energy arc obtained, and from an electrical fan mechanical energy is obtained. This part ACB of the circuit is called external circuit.

vi) Direction of electric current: The potential of the body A (V_{A}) is higher than that of the body B (V_{B}). So in the external circuit i.e., in the part ACB current flows from higher potential to lower potential. But in the source of

electricity i.e., in the internal circuit (in the part BPA) current flows from lower potential to higher potential.