CBSE Class 10 Physics Electricity Notes Set 01

Electric Charge

Charge is a basic property of matter. The SI unit is the coulomb. A body becomes negatively charged when it gains electrons and positively charged when it loses them. The smallest charge is that of one electron, \( e = 1.6 \times 10^{-19} \) C, so any charge is \( q = ne \) (charge is quantised).
Charge is additive, conserved, and does not depend on speed. Like charges repel and unlike charges attract. Coulomb's law gives the force between two point charges: \( F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1q_2}{r^2} \), where \( \dfrac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\ \text{N m}^2/\text{C}^2 \).

Electric Potential and Potential Difference

The potential difference between two points is the work done in carrying a unit positive charge from one point to the other: \( V = W/q \). Its unit is the volt (1 V = 1 J/C). Potential at a point is the work done in bringing a unit positive charge from infinity to that point. Both are scalars. Positive charge moves from high to low potential.
A voltmeter measures potential difference and is connected in parallel across the two points.

Electric Current

Current is the rate of flow of charge: \( I = Q/t \). Its unit is the ampere (1 A = 1 C/s). By convention the current direction is that of positive charge, opposite to the flow of electrons. An ammeter measures current and is connected in series. Current is a scalar.
Metals conduct because of free electrons, insulators have none, and semiconductors conduct better as temperature rises.

Resistance and Resistivity

Resistance is the opposition a conductor offers to the flow of charge; its unit is the ohm. For a conductor of length l and cross-section A: \( R = \rho \dfrac{l}{A} \), where \( \rho \) is the resistivity (unit ohm metre), a property of the material and temperature only.
If a wire is stretched to n times its length, its volume is fixed, so the area falls to 1/n and the resistance rises to \( n^2 \) times. For metals resistance increases with temperature. Alloys such as manganin and constantan change very little with temperature and are used in standard resistors.

Ohm's Law

At constant temperature the current through a conductor is proportional to the potential difference across it: \( V = IR \). The V-I graph is a straight line through the origin. Devices that obey it are ohmic; filament bulbs, diodes and transistors are non-ohmic.
One ohm is the resistance of a conductor that carries 1 A when 1 V is applied across it.

Cell, EMF and Internal Resistance

A cell converts chemical energy into electrical energy. Its EMF E is the work done per unit charge in sending charge round the whole circuit. The electrolyte offers internal resistance r.
Terminal potential difference when the cell discharges: \( V = E - Ir \), with \( I = \dfrac{E}{R + r} \). When it is being charged: \( V = E + Ir \). On open circuit V = E.

Combination of Resistors

For two resistors in parallel, \( R = \dfrac{R_1R_2}{R_1 + R_2} \); n equal resistors R give R/n. The equivalent parallel resistance is always less than the smallest one.
Appliances in houses are connected in parallel because each gets the full voltage, each can be switched off alone, and a fault in one does not stop the others. In series the same current must suit all appliances and one break stops everything.

Kirchhoff's Laws

Junction rule: the algebraic sum of currents meeting at a junction is zero (conservation of charge). Loop rule: in any closed loop the algebraic sum of EMFs equals the sum of the products IR (conservation of energy). For a loop containing a 10 ohm and a 15 ohm branch with a 3 V cell, write the loop equation in each loop and solve the pair together.

Heating Effect and Electric Power

When current flows, electrons collide with ions and lose energy as heat. Heat produced: \( H = I^2Rt = VIt = \dfrac{V^2}{R}t \) joules (Joule's law). In calories divide by 4.18.
Power: \( P = VI = I^2R = \dfrac{V^2}{R} \), unit watt. For a device rated P and V, its resistance is \( R = V^2/P \). Use \( I^2R \) when the same current flows (series) and \( V^2/R \) when the same voltage is applied (parallel).
Commercial unit of energy: 1 kilowatt-hour = 1 unit = \( 3.6 \times 10^{6} \) J. Energy in kWh = power in kW x time in hours.
Uses of heating effect: heater, toaster, iron, electric kettle (coils of high-resistance alloy such as nichrome with a high melting point), and the fuse wire, which melts when the current becomes too large.