Describe the concept and laws of current electricity (electromotive force, potential difference, resistance, effect of electric current, domestic electrical installation)

Electromotive force (e.m.f) is the potential difference across the terminals of a source when no current is flowing. It is the energy provided by a source (such as a battery) to move electrons through a conductor. The SI unit is the volt (V).

Sources of e.m.f include dry cells, car batteries, solar cells, and electric generators. For example, a dry cell has e.m.f of 1.5 V, while a car battery has e.m.f of 12 V.

Potential difference (p.d), also called voltage, is the work done in moving a unit charge between two points in a circuit. It is given by:

$V = \frac{W}{Q}$

where W is work done in joules and Q is charge in coulombs. The SI unit is the volt (V). One volt equals one joule per coulomb.

Difference between e.m.f and p.d: e.m.f is measured across a source when no current flows (no load connected), while p.d is measured when current flows through a load.

Resistance (R) is the opposition to the flow of electric current in a conductor. It is measured in ohms (Ω). Factors affecting resistance include:

• Length: Resistance is directly proportional to length ($R \propto l$)
• Cross-sectional area: Resistance is inversely proportional to area ($R \propto \frac{1}{A}$)
• Temperature: Resistance increases with temperature for most conductors
• Material: Different materials have different resistivities

The relationship between resistance, resistivity, length, and cross-sectional area is:

$R = \frac{\rho l}{A}$

where $\rho$ is resistivity in Ωm.

Ohm's Law

Ohm's law states that the current passing through a conductor is proportional to the potential difference across its ends, provided temperature remains constant:

$V = IR$

Series connection

When resistors are connected end to end, the same current flows through each. Total resistance is the sum:

$R_T = R_1 + R_2 + R_3 + ... + R_n$

Parallel connection

When resistors are placed side by side with ends joined together, the same p.d is across each. The reciprocal of total resistance is:

$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n}$

For n identical resistors in parallel: $R_T = \frac{R}{n}$

A real cell has internal resistance (r) that causes a voltage drop when current flows. The relationship is:

$E = V + Ir$

or

$E = I(R + r)$

where E is e.m.f, V is terminal p.d, R is external resistance, and r is internal resistance.

When current flows through a conductor, electrical energy is converted to heat energy. This is the heating effect of electric current. The heat produced is given by Joule's law:

$H = I^2Rt$

This can also be written as: $H = IVt = \frac{V^2}{R}t$

where H is heat in joules, I is current in amperes, R is resistance in ohms, and t is time in seconds.

Wires and cables

Domestic electricity uses three main wires:

• Live (L): Brown or red, carries current at 240 V
• Neutral (N): Blue or black, returns current
• Earth (E): Yellow or green, for safety

Fuses and circuit breakers

A fuse is a safety device containing a wire that melts when current exceeds its rating, disconnecting the circuit. It is connected in the live wire. Circuit breakers can be reset after tripping.

Three-pin plugs

The earth pin is longer than live and neutral pins. This ensures the appliance is earthed before connecting to power, providing safety against electric shocks.

Ring main and tree systems

• Ring main: A cable forms a loop starting and ending at the consumer unit, allowing current to flow through two paths
• Tree system: Cables branch from a main switch to distribution boxes

Example: A resistor of 100 Ω is connected across a 12 V battery. How much heat is dissipated in 5 seconds?

Solution

Given: R = 100 Ω, V = 12 V, t = 5 s

Using $H = \frac{V^2}{R}t$:

$H = \frac{12^2 \times 5}{100} = \frac{144 \times 5}{100} = 7.2 \text{ J}$

The heat dissipated is 7.2 joules.

In Tanzania, understanding current electricity helps in safely using electrical appliances at home. For example, when purchasing a kettle rated 2000 W for making chai, a student can calculate that it draws a current of about 8.3 A from a 240 V supply ($I = P/V = 2000/240$). This helps in selecting the correct fuse (usually 13 A) and ensuring the wiring can handle the load without causing fires. Knowing about series and parallel connections also helps when arranging multiple bulbs or debugging why some appliances stop working when others are switched on.