Current electricity: Class 10 Physics

Key points

Electric current is the rate of flow of charge through a conductor: I = Q / t. Its unit is the ampere (A), where 1 A = 1 C/s. In a metal, the charge carriers are free electrons. By convention, conventional current is taken in the direction in which positive charge would move, from the positive terminal of a cell to the negative terminal outside the cell. Electrons actually move the other way. Current is measured with an ammeter connected in series.

Potential difference (voltage) between two points is the work done per unit charge: V = W / Q. It is measured in volt with a voltmeter connected in parallel across the component. The electromotive force (e.m.f.) of a cell is the total energy supplied per unit charge by the cell, including the energy lost inside the cell. The terminal voltage is less than the e.m.f. when current flows, because of the internal resistance of the cell.

Ohm's law states that the current through a conductor is directly proportional to the potential difference across its ends, provided its temperature and other physical conditions stay the same: V = I R. The constant R is the resistance. Its unit is the ohm (Ω), where 1 Ω = 1 V/A. A graph of V against I for a metal wire at constant temperature is a straight line through the origin. Such conductors are called ohmic. A filament bulb, a diode and a thermistor do not obey Ohm's law.

The resistance of a wire depends on:

• its length L: R is directly proportional to L,
• its cross-sectional area A: R is inversely proportional to A,
• the material, through a property called resistivity ρ,
• its temperature: for metals resistance rises as temperature rises.

The relation is R = ρ L / A. The resistivity ρ is a property of the material and its unit is the ohm metre (Ω m). Good conductors like copper (about 1.7 × 10⁻⁸ Ω m) have a very small resistivity. Insulators have very large values. A thick wire has less resistance than a thin one of the same length and material, which is why heavy appliances use thick cables.

In a series circuit the components are joined end to end. The same current flows through each one, the voltages add up to the supply voltage, and the total resistance is R = R₁ + R₂ + R₃. If one component breaks, the whole circuit stops. In a parallel circuit the components are joined across the same two points. The voltage across each branch is the same, the currents add up (I = I₁ + I₂), and 1/R = 1/R₁ + 1/R₂ + 1/R₃. The total resistance is less than the smallest branch resistance. Home appliances are connected in parallel so each gets the full supply voltage and works independently.

When a current flows in a resistor, electrical energy changes to heat. This is the heating effect of current. The electrical power is the rate of doing work: P = V I. Using Ohm's law, P = I² R = V² / R. Power is measured in watt (W). The energy used is E = P × t. In joules, E = V I t. In daily life the energy is measured in kilowatt hour (kWh), which is the energy used by a 1 kW device in 1 hour. 1 kWh = 3.6 × 10⁶ J. One kWh is one unit on an electricity bill.

The heating effect is useful in heaters, irons, kettles and electric bulbs. A fuse is a thin wire of low melting point placed in series with the live wire. If the current exceeds a safe value, the fuse melts and breaks the circuit. The fuse rating should be slightly above the normal current of the appliance. Circuit breakers do the same job and can be reset.

Direct current (d.c.) flows in one direction only, as from a cell or battery. Alternating current (a.c.) changes its direction regularly. The mains supply in Pakistan is a.c. at 220 V and 50 Hz, so the current reverses direction 100 times each second. A.c. is used for power distribution because transformers can easily change its voltage.

House wiring and safety:

• A three-pin plug has the live wire (brown), neutral wire (blue) and earth wire (green and yellow).
• The switch and the fuse must be in the live wire so that the appliance is dead when switched off.
• The earth wire joins the metal body of the appliance to the ground. If a fault makes the body live, the current flows to earth through the earth wire, the fuse blows and the user is protected from electric shock.
• Never touch switches with wet hands, and never overload a socket with many appliances.

Study tip: Write the formula first and then substitute with units. Learn the three forms of P = V I = I² R = V² / R and choose the one that uses the values you are given. For circuit questions, draw the diagram and mark the current and voltage in each branch. Learn the colour code of the plug wires and the reason for the earth wire, as these are common five mark questions.

Definitions and flashcards

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Formula sheet

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Short questions with model answers

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Numericals with worked steps

Common mistakes

• Connecting an ammeter in parallel and a voltmeter in series. It is the reverse.
• Adding resistances directly in parallel. Use the reciprocal formula, and check the answer is smaller than the smallest resistor.
• Forgetting to convert area from mm² or cm² to m² in resistivity problems.
• Placing the fuse or switch in the neutral wire instead of the live wire.
• Mixing up kW, W and kWh. Power is in W or kW, energy is in J or kWh.

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