#### [h]Electricity[/h]

**ELECTRIC CURRENT AND CIRCUIT**

**Electric current : **An **electric current** is a flow of **electric **charge. **Electric current** is measured using a device called an ammeter.

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

Electric current is expressed by the amount of charge flowing through a particular area in unit time. In other words, it is the rate of flow of electric 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:-

**Coulomb:- **

The SI unit of electric charge is coulomb (C), which is equivalent to the charge contained in nearly 6 × 10^{18} electrons.

**Ampere** -:

- The electric current is expressed by a unit called ampere (A).
- 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.

**Electric Circuit:-**

- A typical electric circuit comprising a cell, an electric bulb, an ammeter and a plug key.
**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.

[h]**ELECTRIC POTENTIAL AND POTENTIAL DIFFERENCE**[/h]

**Electric potential:-**

The work done to move a unit charge from one point to the other –

- This difference of potential may be produced by a battery, consisting of one or more electric cells.

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

The SI unit of electric potential difference is volt (V).

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.

- The potential difference is measured by means of an instrument called the voltmeter.
- The voltmeter is always connected in parallel across the points between which the potential difference is to be measured.

[h]**CIRCUIT DIAGRAM**[/h]

- A typical electric circuit comprising a cell, an electric bulb, an ammeter and a plug key.
- 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 below :-

[h]**OHM’S LAW**[/h]

It is a relationship between the potential difference across a conductor and the current through it.

**Ohm’s law : **According to 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 flowing through it, provided its temperature remains the same. This is called Ohm’s law.

In other words-:

**Resistivity :-**

In above Equations R is a constant for the given metallic wire at a given temperature and is called its resistance.

**Defination:-** It is the property of a conductor to resist the flow of charges through it. Its SI unit is ohm, represented by the Greek letter Ω.

According to Ohm’s law,

**1 ohm’s:** If 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 Ω. That is,

- current through a resistor is inversely proportional to its resistance. I = V/R

**Variable resistance:-**

A component used to regulate current without changing the voltage source is called variable resistance.

- In an electric circuit, a device called
is often used to change the resistance in the circuit.**rheostat**

[h]**FACTORS ON WHICH THE RESISTANCE OF A CONDUCTOR DEPENDS**[/h]

The resistance of the conductor depends (i) on its length, (ii) on its area of cross-section, and (iii) on the nature of its material.

measurements have shown that resistance of a uniform metallic conductor is directly proportional to its length (l) and inversely proportional to the area of cross-section (A). That is,

where ρ (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor.

The SI unit of resistivity is Ω m. It is a characteristic property of the material.

Both the resistance and resistivity of a material vary with temperature.

[h]**RESISTANCE OF A SYSTEM OF RESISTORS**[/h]

There are two methods of joining the resistors together:-

- Resistors in series and
- Resistors in parallel

### Resistors in series

- Electric circuit in which three resistors having resistances R
_{1}, R_{2}and R_{3}, respectively, are joined end to end. Here the resistors are said to be connected in series. - In a series combination of resistors the current is the same in every part of the circuit or the same current through each resistor.
- 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} - When several resistors are joined in series, the resistance of the combination Rs equals the sum of their individual resistances, R
_{1}, R_{2}, R_{3}, and is thus greater than any individual resistance.

**Disadvantages of series resistance:-**

**Same current everywhere :**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.- Another major disadvantage of a series circuit is that when one component fails the circuit is broken and none of the components works.

### Resistors in parallel

- 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.
- In parallel resistancethe 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} - 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.

[h]**HEATING EFFECT OF ELECTRIC CURRENT**[/h]

If an **electric** circuit is purely resistive (only resistors are connected to a battery), the energy from the source continually gets dissipated totally in the form of **heat**. This **effect** is called as **heating effect of electric current**and it is effectively utilized in **heater**,**electric** iron, **electric** toaster, etc.

[h]Joule’s law of heating[/h]

According to joules law of heating the heat produced in a resistor is

- directly proportional to the square of current for a given resistance,
- directly proportional to resistance for a given current, and
- directly proportional to the time for which the current flows through the resistor.

Mathematical expression for joules law if heating , **H = I ^{2} Rt**

[h]**Practical Applications of Heating Effect of Electric Current**[/h]

- 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 fuse used in electric circuits. It protects circuits and appliances by stopping the flow of any unduly high electric current.

[h]**ELECTRIC POWER**[/h]

It is also the rate of consumption of energy.

The power P is given by

P = VI

Or P = I_{2}R = V_{2}/R

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 × 1 ampere = 1 V A

- The unit ‘watt’ is very small. Therefore, in actual practice we use a much larger unit called ‘kilowatt’. It is equal to 1000 watts. Since electrical energy is the product of power and time, the unit of electric energy is, therefore, watt hour (W h).
- One 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 × 3600 second

= 3.6 × 106 watt second

= 3.6 × 106 joule (J)