Electric Resistance and Ohm's Law

1.0Electric Resistance

The property of a material which offers opposition to the electric current and dissipates energy is called its ‘electric resistance’.

The ratio of applied potential difference (voltage) to the resulting electric current in a closed circuit is called ‘electric resistance’.

$R=\frac{V}{I}$

Unit of Resistance 

SI unit : ohm (Ω)

1 ohm = 1 volt/ampere or   1 Ω = 1 V A^–1

Definition of 1 ohm

When the potential difference of 1 volt is applied across the ends of a conductor and the current produced in it is 1 ampere, then the resistance of the conductor is 1 ohm.

Voltage and Resistance

See the water filled bucket in the figure below. The raised water has energy that is lost when the water falls. Increasing the height from which the water falls increases the energy of the water.

Increasing the height of the water is similar to increasing the voltage of the battery. Just as the water current increases when the height of the water increases, the electric current in a circuit increases as voltage increases.

2.0Ohm’s law

(given by German physicist George Simon Ohm in 1827)

According to Ohm’s law, ‘the current through certain conductors is directly proportional to the potential difference between its ends at a constant temperature’.(see figure (a) and (b))

$I\propto VorV\propto I$

$orV=IR$

or $R=\frac{V}{I}$ Where, R is constant called resistance of the conductor.        

Ohm’s law is not a fundamental law, it is only an empirical law that holds approximately good for many substances particularly metals. (see figure)

3.0Electric Circuits

A continuous path which consists of various electric devices like bulb, tube light, resistors, etc. connected with each other through conducting wires to the terminals of a source of voltage like battery is called electric circuit.

Circuit elements

The various devices like electric bulbs, resistors, etc. connected in an electric circuit are called circuit elements. (see figure)

Circuit diagram

A diagram which indicates how different devices are connected in a circuit by using proper electric symbols for the devices is called a circuit diagram.

Symbols of some commonly used components in circuit diagrams

1. If the current in a household appliance is 5 A, calculate the amount of charge that passes through the appliance in 1 hour.

Solution

Given, current, I = 5 A ; time, t = 1 h = 3600 s ; charge. Q=? 

Now, charge, Q = I × t = 5 × 3600 = 18000 C = 1.8 × 10⁴ C

2. In a particular television tube, a beam of electrons is emitted. The beam current is 80 μA. How many electrons strike the screen of TV every second? Also find the total charge striking the screen in 2 minutes.

Solution

Here, I = 80 μA= 80 × 10^–6 A = 8 × 10^–5 A

(i) t = 1 second

Using, $I=\frac{Q}{t}=\frac{ne}{t}$ , we get

$n=\frac{It}{e}=\frac{8\times 10^{-5}A\times 1s}{1.6\times 10^{-19}C}=5\times 10^{14}$ (Q e = 1.6 × 10^–19 C) 

∴ 5 × 10¹⁴ electrons strike the screen every second.

(ii) Also, $I=\frac{Q}{t}$

∴ Q = It = 8 × 10^–5 A × 2 minutes = 8 × 10^–5 A × 2 × 60 seconds

= 960 × 10^–5 C = 9600 × 10^–6 C = 9600 μC

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