Current Electricity

Q: A wire of resistance 10 Ω is cut into two equal halves, and the halves are joined in parallel. What is the new resistance? Does the resistivity change?

Each half has 5 Ω. In parallel, Rp = 5/2 = 2.5 Ω. The resistivity does not change, because it depends only on the material and its temperature.

ICSE Class 10 · Physics · Chapter 8

What this chapter covers

Charge, current and potential difference
Resistance
Ohm's law
Ohmic and non-ohmic resistors
Factors affecting resistance and specific resistance
Electromotive force and internal resistance
Resistances in series
Resistances in parallel
Electrical energy and electrical power
The commercial unit of electrical energy

Key definitions

Electric charge is the property of matter because of which a body experiences a force in an electric field.

Electric current is the rate of flow of electric charge through any cross-section of a conductor.

One ampere is the current in a conductor when a charge of one coulomb flows through any cross-section of it in one second.

Conventional current is the current imagined to flow from the higher potential to the lower potential in the external circuit.

One volt is the potential difference between two points when one joule of work is done in moving one coulomb of charge from one point to the other.

Resistance is the property of a conductor by which it opposes the flow of current through it.

One ohm is the resistance of a conductor through which a current of one ampere flows when a potential difference of one volt is applied across its ends.

Ohmic resistors are conductors that obey Ohm's law, so that their V-I graph is a straight line through the origin.

Non-ohmic resistors are conductors that do not obey Ohm's law, so that their V-I graph is not a straight line.

Superconductivity is the property by which certain materials lose all electrical resistance when cooled below a particular temperature.

A superconductor is a material that shows superconductivity, and the temperature at which its resistance vanishes is called its critical temperature.

Internal resistance is the resistance offered by the electrolyte and electrodes of a cell to the flow of current through the cell.

Key points

Electric current is the rate of flow of charge, I = Q/t; its SI unit is the ampere, and it is measured with an ammeter connected in series.
Potential difference is the work done per unit charge, V = W/Q; its SI unit is the volt, and it is measured with a voltmeter connected in parallel.
Resistance is the opposition a conductor offers to current, R = V/I, measured in ohms.
Ohm's law: V ∝ I at constant temperature, so V = IR; the V-I graph of an ohmic conductor is a straight line through the origin, and its slope is the resistance.
Non-ohmic conductors, such as a filament lamp and a junction diode, have a curved or one-sided V-I graph.
Resistance depends on length, area of cross-section, material and temperature: R = ρ l/a.
Specific resistance (resistivity) ρ depends only on the material and temperature; its SI unit is Ω m.
A superconductor has zero resistance below its critical temperature.
The emf of a cell is the work done per unit charge in the whole circuit; terminal voltage V = mathcalE - Ir, and I = mathcalE/(R + r).
In series: same current, voltages add, R_s = R₁ + R₂ + R₃, larger than the largest resistor.
In parallel: same voltage, currents add, 1/R_p = 1/R₁ + 1/R₂ + 1/R₃, smaller than the smallest resistor.
Electrical energy W = QV = VIt = I²Rt = (V²/R)t, in joules.
Electrical power P = W/t = VI = I²R = V²/R, in watts.
The commercial unit of energy is the kilowatt hour: 1 kW h = 3.6 × 10⁶ J, and energy in kW h = power in kW × time in h.

Questions answered

Define electric current and state its SI unit. How much charge flows when a current of 2 A passes for one minute?

Electric current is the rate of flow of charge through a cross-section of a conductor; its SI unit is the ampere. Q = It = 2 × 60 = 120 C.

Define one volt.

One volt is the potential difference between two points when one joule of work is done in moving one coulomb of charge from one point to the other.

State Ohm's law. Why is the condition about temperature necessary?

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. The condition is needed because the resistance of a conductor changes with temperature; if the wire heats up, V/I changes and the proportionality fails.

On a V-I graph, line A is steeper than line B. Both pass through the origin. Which conductor has the greater resistance? Give a reason.

A. The slope of a V-I graph equals the resistance, so the steeper line belongs to the conductor with greater resistance.

Name one ohmic and two non-ohmic conductors. Describe the V-I graph of a filament lamp.

Ohmic: a nichrome wire at constant temperature. Non-ohmic: a filament lamp and a junction diode. For a filament lamp the graph is a curve that gets steeper as the current increases, because the filament's resistance rises as it gets hotter.

A wire of resistance 10 Ω is cut into two equal halves, and the halves are joined in parallel. What is the new resistance? Does the resistivity change?

Each half has 5 Ω. In parallel, R_p = 5/2 = 2.5 Ω. The resistivity does not change, because it depends only on the material and its temperature.

Why is nichrome used for the element of an electric heater, but copper for connecting wires?

Nichrome has a high resistivity, so a short coil produces a lot of heat; it also does not oxidise easily when red-hot. Copper has a very low resistivity, so connecting wires waste very little energy as heat.

What is a superconductor? Give one use.

A superconductor is a material whose resistance becomes zero when it is cooled below its critical temperature. It is used to make very strong electromagnets, for example in MRI scanners.

Past board exam questions

ICSE 2027 sample paper · 4 marks

A Nichrome wire X with length (l) and cross-sectional area (A) is connected to a 10 V source and another Nichrome wire Y with length (2l) and cross-sectional area (A/2), is connected to a 20 V source. (a) Compare the resistances of wires X and Y. [Given that the resistivity of Nichrome is (ρ).] (b) Compare the electrical power consumed by each wire. (c) Compare the masses of these wires. [Given that the density of nichrome is d.] (d) State True or False: Wire X and wire Y both show the same rise in temperature at the same time.

Show answer

(a) R_X = (ρ l)/(A), R_Y = (ρ (2l))/(A/2) = (4ρ l)/(A), so R_X : R_Y = 1 : 4. (b) P_X = (10²)/(R), P_Y = (20²)/(4R) = (100)/(R), so P_X : P_Y = 1 : 1. (c) m_X = A l d, m_Y = (A)/(2) × 2l × d = A l d, so m_X : m_Y = 1 : 1. (d) True. Heat produced in time t: Q = Pt = mcΔ T; P, t, m and c are the same for both wires, so the rise in temperature ΔT is the same.

ICSE 2027 sample paper · 3 marks

Three bulbs of powers P₁, P₂ and P₃ (P₁<P₂<P₃) are connected in a certain way such that P₃ glows the brightest. (a) What type of connection exists between these bulbs? (b) Compare the voltages (V₁, V₂, V₃) across these bulbs. (Use >, < or =) (c) Will the circuit still function if one of the bulbs is fused?

Show answer

(a) Parallel – only in parallel (same voltage) does the bulb of highest rated power consume the most power and glow brightest. (b) V₁ = V₂ = V₃. (c) Yes – each bulb is in a separate branch, so the other bulbs keep glowing.

ICSE 2026 board paper · 1 mark

In the circuit described below, identify the lamp (L1, L2, L3 or L4) whose failure would not interrupt the power supply to the other lamps. One terminal of a cell is connected through lamp L1 to a junction P. From P, lamp L2 is connected directly back to the other terminal of the cell. Also from P, lamps L3 and L4 are connected one after the other back to that same terminal of the cell.

Show answer

ICSE 2026 sample paper · 1 mark

In a circuit, a 12 V cell is connected across two branches in parallel: one branch has a 3 Ω resistor in series with a 2 Ω resistor, and the other branch has a single 5 Ω resistor. Identify the correct relation between the currents flowing through the 2 Ω, 3 Ω, and 5 Ω resistors:

current through 2Ω > current through 3Ω
current through 5Ω < current through 3Ω
current through 2Ω = current through 5Ω
current through 5Ω > current through 3Ω

Show answer

current through 2Ω = current through 5Ω

ICSE 2026 board paper · 1 mark

The correct formula to calculate the equivalent resistance of two resistors R₁ and R₂ when connected in parallel, is:

(R₁ + R₂)/(R₁ R₂)
(R₁ R₂)/(R₁ + R₂)
(R₁ - R₂)/(R₁ R₂)
(R₁ R₂)/(R₁ - R₂)

Show answer

(R₁ R₂)/(R₁ + R₂)

ICSE 2026 sample paper · 2 marks

The kilowatt-hour meter readings recorded at two distinct points in time are shown below. | | First reading | Second reading | |---|---|---| | KWH meter | 00856 | 01567 | Assuming a continuously running 2000W air conditioner as the sole electrical device in use, calculate the time interval, in hours, between these two meter readings.

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Energy consumed = 01567 − 00856 = 711 kWh Power = 2000 W = 2 kW Time = Energy / Power = 711 kWh ÷ 2 kW = 355.5 hours

ICSE 2026 board paper · 2 marks

A resistance R is connected across a cell with a switch and a rheostat in series. A voltmeter is connected parallel across the cell. Current in the circuit is increased using the rheostat. (a) How will the voltmeter reading change? (increase / decrease / remain the same) (b) Justify your answer stated in (a) above.

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(a) The voltmeter reading will decrease. (b) The voltmeter reads the terminal voltage V = ε − Ir, where r is the internal resistance of the cell. When the current I increases, the potential drop Ir inside the cell increases, so the terminal voltage decreases.

ICSE 2026 sample paper · 3 marks

Three bulbs of powers P₁, P₂ and P₃ (P₁<P₂<P₃) are connected in a certain way that P₃ glows brightest. (a) What type of connection exists between these bulbs? (b) Compare the voltage across these bulbs. (Use >, < or =) (c) Will the circuit still function if one of the bulbs is fused?

Show answer

(a) Parallel. (In parallel each bulb gets the same voltage, so the bulb of highest power rating, P₃, glows brightest; in series the lowest-power bulb would glow brightest.) (b) V₁ = V₂ = V₃ (c) Yes — the other bulbs keep glowing, because each is on its own branch connected directly across the supply.