## 12.1 ELECTRIC CURRENT AND CIRCUIT

**Electric circuit**: A continuous and closed path of an electric current is called an electric circuit.

The electric current was considered to be the flow of positive charges and the direction of flow of positive charges was taken to be the direction of electric current.

Conventionally, in an electric circuit the direction of electric current is taken as opposite to the direction of the flow of electrons, which are negative charges.

If a net charge Q, flows across any cross-section of a conductor in time t, then the current I, through the cross-section is given by

I = \frac{Q}{t} . . . . . . . 12.1- The SI unit of electric charge is
**coulomb**(C). - 1 Coulomb is equivalent to the charge contained in nearly 6 \times 10^{18} electrons.
- An electron possesses a negative charge of 1.6 \times 10^{-19} C
- The electric current is expressed by a unit called
**ampere**(A). It named after the French scientist,**Andre-Marie Ampere**(1775–1836). - One ampere is constituted by the flow of one coulomb of charge per second, that is, 1 A = 1 C/1 s.
- Small quantities of current are expressed in milliampere. (1 mA = 10^{-3} A) or in microampere (1 μA = 10^{-6} A).
- An instrument called ammeter measures electric current in a circuit. It is always connected in series in a circuit through which the current is to be measured.
- Note that the electric current flows in the circuit from the positive terminal of the cell to the negative terminal of the cell through the bulb and ammeter.

## 12.2 ELECTRIC POTENTIAL AND POTENTIAL DIFFERENCE

For flow of charges in a conducting metallic wire, the gravity, of course, has no role to play.

**Potential Difference**: The electrons move only if there is a difference of electric pressure, called the ** potential difference** along the conductor.

- This difference of potential may be produced by a battery, consisting of one or more electric cells. The chemical action within a cell generates the potential difference across the terminals of the cell, even when no current is drawn from it.
- When the cell is connected to a conducting circuit element, the potential difference sets the charges in motion in the conductor and produces an electric current.
- In order to maintain the current in a given electric circuit, the cell has to expend its chemical energy stored in it.

Potential difference (V) between two points = Work done (W)/Charge (Q)

V = \frac{W}{Q} . . . . . . . 12.2- The SI unit of electric potential difference is
**volt**(V). It named after**Alessandro Volta**(1745–1827), an Italian physicist. - One volt is the potential difference between two points in a current carrying conductor when 1 joule of work is done to move a charge of 1 coulomb from one point to the other.

Therefore,

1 Volt = \frac{1 joule}{1 coulomb} . . . . . . . 12.3 1 V = 1 J C^{-1}- The potential difference is measured by an instrument called the
**voltmeter**. - The
**voltmeter is always connected in parallel**across the points between which the potential difference is to be measured.

## 12.3 CIRCUIT DIAGRAM

An electric circuit comprises a cell (or a battery), a plug key, electrical component(s), and connecting wires.

It is often convenient to draw a schematic diagram, in which different components of the circuit are represented by the symbols conveniently used. Conventional symbols used to represent some of the most commonly used electrical components are given in table below.

## 12.4 OHM’S LAW

The potential difference, V, across the ends of a given metallic wire in an electric circuit is directly proportional to the current, I, flowing through it, while its temperature remains the same. This is called **Ohm’s law**.

Ohm’s law tells a relationship between the potential difference across a conductor and the current through it.

In 1827, a German physicist **Georg Simon Ohm** (1787–1854) found out the relationship between the current I, flowing in a metallic wire and the potential difference across its terminals.

Mathematically, Ohm’s law given by,

V \propto I . . . . . . . . . 12.4 \Rightarrow V/I = Constant \Rightarrow V/I = R \Rightarrow V = IR . . . . . . . . . 12.5Here,

- R is a constant for the given metallic wire at a given temperature and is called its
**resistance**. - R is the property of a conductor to resist the flow of charges through it.
- Its SI unit is ohm, represented by the Greek letter \Omega.

According to Ohm’s law,

R = V/I . . . . . . . . . 12.6If the potential difference across the two ends of a conductor is 1 V and the current through it is 1 A, then the resistance R, of the conductor is 1 \Omega.

That is,

1 ohm = \frac{1 volt}{1 ampere} 1 \Omega = \frac{1 V}{1 A}If ,

V = IR \Rightarrow I = V/R . . . . . . . . . 12.7- The current through a resistor is inversely proportional to its resistance.
- If the resistance is doubled the current gets halved.
- A component used to regulate current without changing the voltage source is called
**variable resistance**. - In an electric circuit, a device called
**rheostat**is often used to change the resistance in the circuit. - The motion of electrons through a conductor is retarded by its resistance.
- A component of a given size that offers a
**low resistance**is a**good conductor**. - A conductor having some appreciable resistance is called a resistor.
- A component of identical size that offers a
**higher resistance**is a**poor conductor**. - An insulator of the same size offers even higher resistance.

## 12.5 FACTORS ON WHICH THE RESISTANCE OF A

CONDUCTOR DEPENDS

- The ammeter reading decreases to one-half when the length of the wire is doubled.
- The ammeter reading is increased when a thicker wire of the same material and of the same length is used in the circuit.
- A change in ammeter reading is observed when a wire of different material of the same length and the same area of cross-section is used.

The resistance of the conductor depends

- (i) on its length,
- (ii) on its area ofcross-section, and
- (iii) on the nature of its material.

The resistance of a uniform metallic conductor is directly proportional to its length (l ) and inversely proportional to the area of cross-section (A).

Mathematically,

R \propto l . . . . . . . . . 12.8 V \propto \frac{1}{A} . . . . . . . . . 12.9By combining eqations 12.8 and 12.9, we found,

R \propto \frac{l}{A} \Rightarrow R = \rho \frac{l}{A} . . . . . . . . . 12.10Here,

- r (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor.
- The SI unit of resistivity is \Omega m. It is a characteristic property of the material.
- The metals and alloys have very low resistivity in the range of 10 ^{-8}\Omega m to 10^{-6}\Omega m. They are good conductors of electricity.
- Insulators like rubber and glass have resistivity of the order of 10^{12}\Omega m to 10^{17}\Omega m. Both the resistance and resistivity of a material vary with temperature.
- Alloys do not oxidise (burn) readily at high temperatures. For this reason, they are commonly used in electrical heating devices, like electric iron, toasters etc.
**Tungsten**is used almost exclusively for filaments of**electric bulbs**, whereas copper and aluminium are generally used for electrical transmission lines.

Electrical resistivity* of some substances at 20°C (Table)

## 12.6 RESISTANCE OF A SYSTEM OF RESISTORS

There are two methods of joining the resistors together.

(i) Resisters in series

(ii) Resisters in parallel

An electric circuit in which three resistors having resistances R1, R2 and R3, respectively, are joined end to end. Here the resistors are said to be connected in series.

A combination of resistors in which three resistors are connected together between points X and Y. Here, the resistors are said to be connected in parallel.

### 12.6.1 Resistors in Series

- The current in the ammeter is same, independent of its position in the electric circuit.
- In a series combination of resistors the current remains same in every part of the circuit or the same current through each resistor.

- The potential difference V is equal to the sum of potential differences V1, V2, and V3.
- The total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors.

That is,

V = V_{1} + V_{2} + V_{3} . . . . . . . . . 12.11I = be the current through the circuit.

Also, I = current through each resistor

It is possible to replace the three resistors joined in series by an equivalent single resistor of resistance R, such that the potential difference V across it, and the current I through the circuit remains the same.

Applying the Ohm’s law to the entire circuit, we have

V = IROn applying Ohm’s law to the three resistors separately, we further have

V_{1} = IR_{1} . . . . . . . 12.13(a) \Rightarrow V_{2} = IR_{2} . . . . . . . 12.13(b) \Rightarrow V_{3} = IR_{3} . . . . . . . 12.13(c)From equation 12.11, we got,

IR = IR_{1} + IR_{2} + IR_{3} \Rightarrow R_{s} = R_{1} + R_{2} + R_{3} . . . . . . . 12.14#### Conclusion:

When several resistors are joined in series, the resistance of the combination Rs equals the sum of their individual resistances, R1, R2, R3, and is thus greater than any individual resistance.

#### Advantage of a series circuit

In a series circuit the current is constant throughout the electric circuit. Thus it is obviously impracticable to connect an electric bulb and an electric heater in series, because they need currents of widely different values to operate properly.

#### Disadvantage of a series circuit

- In the series combination when one component fails the circuit is broken and none of the components works.
- If we have used ‘fairy lights’ to decorate buildings on festivals, on marriage celebrations etc., you might have seen the electrician spending lot of time in trouble-locating and replacing the ‘dead’ bulb – each has to be tested to find which has fused or gone.

### 12.6.2 Resistors in Parallel

Let us consider the arrangement of three resistors joined in parallel with a combination of cells (or a battery).

The total current I, is equal to the sum of the separate currents through each branch of the combination.

I = I_{1} + I_{2} + I_{3}Let Rp = the equivalent resistance of the parallel combination of resistors. We have,

I = \frac{V}{R_{p}} . . . . . . . . . 12.16By applying Ohm’s law to the parallel combination of resistors,

We have,

From equations 12.15, 12.16, 12.17(a), 12.17(b, 12.17(c) we got,

\frac{V}{R_{p}} = \frac{V}{R_{1}} + \frac{V}{R_{2}} + \frac{V}{R_{3}} \Rightarrow \frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}#### Conclusion:

The reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.

#### Advantage of a parallel circuit

Parallel connection is helpful particularly when each gadget has different resistance and requires different current to operate properly.

#### Disadvantage of a parallel circuit

- In a parallel circuit divides the current through the electrical gadgets.
- The total resistance in a parallel circuit is decreased.

## 12.7 HEATING EFFECT OF ELECTRIC CURRENT

When the electric circuit is purely resistive, that is, a configuration of resistors only connected to a battery; the source energy continually gets dissipated entirely in the form of heat. This is known as the **heating effect of electric current**.

This effect is utilised in devices such as electric heater, electric iron etc.

Consider,

I = current I flowing through a resister.

R = resistance of the resister

V = potential difference across circuit

t = the time period during a charge flows

Q = charge flows across the circuit

The work done in moving the charge Q through a potential difference V is VQ.

Therefore, the source must supply energy equal to VQ in time t. Hence the power input to the circuit by the source is

The energy supplied to the circuit by the source in time t is P × t, that is, VIt. This

energy gets dissipated in the resistor as heat. Thus for a steady current I, the amount of heat H produced in time t is,

By applying Ohm’s law V = IR,

\Rightarrow H = I^{2}Rt . . . . . . . . . 12.21This is known as **Joule’s law of heating**.

heat produced in a resistor is

(i) directly proportional to the square of current for a given resistance.

(ii) directly proportional to resistance for a given current, and

H \propto R(iii) directly proportional to the time for which the current flows through the resistor.

H \propto tIn practical situations, when an electric appliance is connected to a known voltage source is used after calculating the current through it, using the relation I = V/R.

### 12.7.1 Practical Applications of Heating Effect of Electric Current

The heating effect of electric current has many useful applications. The electric laundry iron, electric toaster, electric oven, electric kettle and electric heater are some of the familiar devices based on Joule’s heating.

- The electric heating is also used to produce light, as in an electric bulb.
- The filament must retain as much of the heat generated as is possible, so that it gets very hot and emits light. It must not melt at such high temperature.
- A strong metal with high melting point such as tungsten (melting point
**3380°C**) is used for making bulb filaments. The filament should be thermally isolated as much as possible, using insulating support, etc. The bulbs are usually filled with chemically inactive nitrogen and argon gases to prolong the life of filament. - Most of the power consumed by the filament appears as heat, but a small part of it is in the form of light radiated.
- Another common application of Joule’s heating is the fuse used in electric circuits. It protects circuits and appliances by stopping the flow of any unduly high electric current.
- The fuse is placed in series with the device. It consists of a piece of wire made of a metal or an alloy of appropriate melting point, for example aluminium, copper, iron, lead etc.
- If a current larger than the specified value flows through the circuit, the temperature of the fuse wire increases. This melts the fuse wire and breaks the circuit.
- The fuse wire is usually encased in a cartridge of porcelain or similar material with metal ends. The fuses used for domestic purposes are rated as 1 A, 2 A, 3 A, 5 A, 10 A, etc.

For an electric iron which consumes 1 kW electric power when operated at 220 V, a current of (1000/220) A, that is, 4.54 A will flow in the circuit. In this case, a 5 A fuse must be used.

## 12.8 ELECTRIC POWER

The rate at which electric energy is dissipated or consumed in an electric circuit is called as **electric power**.

Mathematically,

P = VI

\Rightarrow P = I^{2}R \Rightarrow P = \frac{V^{2}}{R} . . . . . . . . . 12.22- The SI unit of electric power is watt (W).
- It is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V. Thus,

1 W = 1 Volt X 1 Ampere

\Rightarrow 1 W = 1 V A . . . . . . . . . 12.23

- The unit ‘watt’ is very small.
- Therefore, in actual practice we use a much larger unit called ‘kilowatt’.
- 1 Kilowatt = 1000 watts.
- Electrical energy is the product of power and time, the unit of electric energy is, watt hour (W h).
- One(1) watt hour is the energy consumed when 1 watt of power is used for 1 hour. The commercial unit of electric energy is kilowatt hour (kW h), commonly known as ‘unit’.

1 kW h = 1000 watt X 3600 Second

1 kW h = 3.6 X 10^{8} watt second

1 kW h = 3.6 X 10^{8} Joule(J)

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