Electricity
CBSE Class 10 · Science · Notes, formulas and practice questions
Electricity in Class 10 builds one chain of ideas: charge moves, that movement is current, something must push it, and something resists it. Ohm's law ties those together, and everything after it — series and parallel circuits, heating, power — is that one relationship applied.
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The chapter opens with electric current as a rate: how much charge passes a point each second. Potential difference is what makes that happen — the work done moving each unit of charge between two points. If current is the flow, potential difference is the reason there is a flow at all, and it helps to keep those two roles separate from the start, because most confusion in this chapter is really the two being mixed up.
Ohm's law then states the relationship between them for a conductor at constant temperature: current is proportional to potential difference, and the constant of proportionality is resistance. Resistance itself is not arbitrary — it depends on what the conductor is made of, how long it is and how thick it is, which is where resistivity comes in as the material's own property, independent of the particular piece of wire.
Circuits are then two arrangements. In series, the same current passes through every component and the potential differences add, so resistances add directly. In parallel, every component sits across the same potential difference and the currents add, so it is the reciprocals of the resistances that add. Almost every numerical in this chapter is decided by correctly identifying which of the two you are looking at.
Finally, current through a resistance produces heat, and the rate at which it does so is power. The joule heating relationship explains the filament of a bulb, the element of a heater, and why a fuse of the right rating melts before the wiring does. Domestic wiring — live, neutral and earth, and why appliances are connected in parallel — is the practical end of the same physics.
Key terms
- Electric current
- The rate of flow of electric charge through a cross-section of a conductor. Measured in amperes; one ampere is one coulomb per second. Conventional current is taken as the direction positive charge would move, which is opposite to the actual drift of electrons.
- Potential difference
- The work done to move one unit of charge between two points in a circuit. Measured in volts; one volt is one joule per coulomb. It is what drives current, not what current is.
- Resistance
- A conductor's opposition to current. Measured in ohms. For a given conductor at constant temperature it is the ratio of potential difference to current.
- Resistivity
- A property of the MATERIAL rather than of a particular wire. Resistance depends on length and cross-sectional area as well; resistivity is what remains when those are accounted for, which is why it is used to compare materials.
- Series arrangement
- Components joined end to end, so the same current passes through each. The potential differences across them add, and the equivalent resistance is the sum of the individual resistances — always larger than the largest one.
- Parallel arrangement
- Components joined across the same two points, so each has the same potential difference. The currents through them add, and the reciprocal of the equivalent resistance is the sum of the reciprocals — so the equivalent is always smaller than the smallest one.
- Joule heating
- The production of heat when current passes through a resistance. The heat produced grows with the square of the current, which is why a small increase in current has a large effect, and why fuses and appliance ratings matter.
- Electric power
- The rate at which electrical energy is converted to another form. Measured in watts. The commercial unit of energy, the kilowatt-hour, is power multiplied by time, which is what an electricity bill actually charges for.
Formula sheet
| What | Formula | Notes |
|---|---|---|
| Electric current | I = Q/t | Q is charge in coulombs, t is time in seconds, I is current in amperes. |
| Potential difference | V = W/Q | W is work done in joules, Q is charge in coulombs, V is potential difference in volts. |
| Ohm's law | V = IR | Valid for a conductor at constant temperature. R is resistance in ohms (Ω). |
| Resistance of a conductor | R = ρL / A | ρ (rho) is resistivity, L is length, A is cross-sectional area. Longer means more resistance; thicker means less. |
| Resistances in series | R = R₁ + R₂ + R₃ + … | Same current through each; potential differences add. |
| Resistances in parallel | 1/R = 1/R₁ + 1/R₂ + 1/R₃ + … | Same potential difference across each; currents add. |
| Heat produced (Joule's law) | H = I²Rt | Note the SQUARE on the current — doubling the current gives four times the heat. |
| Electric power | P = VI = I²R = V²/R | Use whichever form matches the quantities you were given. |
| Commercial unit of energy | 1 kWh = 3.6 × 10⁶ J | One unit on an electricity bill is one kilowatt-hour. |
Practice questions with answers
1. What is meant by saying that the potential difference between two points is 1 volt?
It means 1 joule of work is done in moving a charge of 1 coulomb from one point to the other. Volt is defined as joule per coulomb, so the statement is about energy per unit charge, not about how much charge is flowing.
2. How much current flows through a conductor if 30 C of charge passes a point in 10 s?
Current is charge divided by time, so I = 30 / 10 = 3 A.
3. A 12 V battery drives a current of 2.4 A through a resistor. What is its resistance?
From Ohm's law, R = V / I = 12 / 2.4 = 5 ohms.
4. Two resistors of 4 ohms and 6 ohms are joined in series across a 20 V supply. Find the current.
In series the resistances add: R = 4 + 6 = 10 ohms. Then I = V / R = 20 / 10 = 2 A. The same 2 A passes through both resistors.
5. The same 4 ohm and 6 ohm resistors are now joined in parallel across the same 20 V supply. Find the total current.
In parallel, 1/R = 1/4 + 1/6 = 5/12, so R = 2.4 ohms. Total current I = 20 / 2.4 = 8.33 A. Note it is much larger than in series, and the equivalent resistance is smaller than either resistor.
6. Why are appliances in a house connected in parallel rather than in series?
Three reasons. Each appliance then gets the full supply voltage it is designed for; each can be switched on and off independently; and a fault in one does not break the circuit for the others. In series they would share the voltage, all switch together, and one failure would stop everything.
7. Why does the connecting cord of an electric heater not glow while the heating element does?
The same current passes through both, and heat produced is proportional to resistance for a given current. The element is made of a high-resistance alloy, so it dissipates a great deal of heat and glows; the copper cord has very low resistance and dissipates very little.
8. How does the resistance of a wire change if its length is doubled and its area of cross-section is halved?
Resistance is proportional to length and inversely proportional to area. Doubling the length doubles it; halving the area doubles it again. So the resistance becomes four times the original.
9. An electric bulb is rated 100 W, 220 V. Calculate its resistance and the current it draws.
From P = V²/R, the resistance is R = V²/P = (220 × 220) / 100 = 484 ohms. The current it draws is I = P/V = 100/220 ≈ 0.45 A.
10. Why is tungsten used for the filament of an electric lamp?
Tungsten has a very high melting point and high resistivity, so the filament can reach the temperature at which it glows brightly without melting, and it produces enough heat at that current to do so.
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