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State Board · Class 9 · Science and Technology

Lesson 3: Current Electricity

5 concepts · 40 practice questions with answers · Free to read

This lesson is also in: मराठी

Potential and potential difference

From daily life

Water in a tank on the terrace flows down the pipe to your tap because the tank is higher. If the tank and the tap were at the same height, nothing would flow. Charge in a wire behaves the same way: it needs a difference in electric level.

Simple definition

Potential difference (विभवांतर) is the work done per unit charge to move charge between two points: V = W ÷ Q.

Water flowing from a high tank to a low tank compared with charge flowing in a circuit with a cell and a bulbhigh levellow levelWater flows from high to low+−💡Charge flows from highto low potentialPotential difference is like a difference of water level

In the figure : In the figure potential difference is like a difference in water level that makes water flow.

Rule 1: Potential and flow of charge — Charge flows because of a difference in electric potential (विद्युत विभव), like water levels. Positive charge flows from high to low potential, and electrons flow from low to high.

  • Easy : A 1.5 V cell has its + end at higher potential; electrons go from the − end to the + end through the wire.
  • Medium : If both ends of a wire are at the same potential, no current flows, like water in a pipe with no height difference.
  • Exam-type : A cell's potential difference comes from chemical reactions inside it. Volta made the first cell.

Rule 2: The volt — V = W ÷ Q. The unit is the volt (V), and 1 V = 1 J/C.

  • Easy : 6 J of work moves 2 C: V = 6 ÷ 2 = 3 V.
  • Medium : A 12 V battery gives 12 J to each coulomb that passes.
  • Exam-type : 24 J of work is done in moving a charge between two points at 6 V. Q = W ÷ V = 24 ÷ 6 = 4 C.
Remember

V = W ÷ Q; unit volt, 1 V = 1 J/C. Charge flows from high to low potential (positive charge).

Common mistake

Saying current flows because of a battery's charge. It flows because of potential difference.

Shortcut

Memory clue: "Water level = Potential, Water flow = Current".

Spot the difference

IdeaWaterElectricity
PushHeight differencePotential difference
FlowWater flowCurrent
UnitMetreVolt

Practice questions

Easy
  1. 1What is potential difference?
  2. 2Write the formula of potential difference.
  3. 3What is the SI unit of potential difference?
Medium
  1. 4Who made the first cell?
  2. 5From where does the potential difference of a cell come?
  3. 610 J of work moves 5 C. Find V.
Challenging
  1. 7How much work is done in moving 4 C across 9 V?
  2. 8Explain with the water analogy why no current flows when both ends of a wire are at the same potential.
Show answers (try them yourself first)
  1. 1The work done per unit charge in moving charge between two points.
  2. 2V = W ÷ Q
  3. 3Volt (1 V = 1 J/C)
  4. 4Volta
  5. 5From chemical reactions inside the cell.
  6. 610 ÷ 5 = 2 V
  7. 7W = V × Q = 9 × 4 = 36 J
  8. 8Like two tanks at the same water level, there is no push to move the charge.

Electric current and free electrons

From daily life

A crowd moving through a gate: if 300 people pass in 60 seconds, the rate of flow is 5 people per second. Electric current is the same idea, counting charge instead of people.

Simple definition

Electric current (विद्युतप्रवाह) is the rate of flow of charge: I = Q ÷ t.

Rule 1: Current and free electrons — Free electrons (मुक्त इलेक्ट्रॉन) carry the current in metals. I = Q ÷ t, and the unit is the ampere (A), where 1 A = 1 C/s. The charge of an electron is 1.6 × 10−19 C. Conventional current flows from + to −, which is opposite to the electron flow.

  • Easy : 10 C flows in 5 s: I = 10 ÷ 5 = 2 A.
  • Medium : A 0.5 A current flows for 20 s: Q = I × t = 0.5 × 20 = 10 C.
  • Exam-type : Number of electrons in 3.2 C: 3.2 ÷ (1.6 × 10⁻¹⁹) = 2 × 10¹⁹ electrons.

Rule 2: Direction of current — Early scientists said current flows from + to − (conventional current). We now know that electrons flow from − to +. Both descriptions are used, and the direction of the current is always taken from + to − in circuits.

  • Easy : In a torch, electrons move from the cell's − end through the bulb to the + end, but the current is said to go from + to −.
  • Medium : The charge of 5 electrons is 5 × 1.6 × 10⁻¹⁹ = 8 × 10⁻¹⁹ C.
  • Exam-type : A current of 2 A for 10 minutes: t = 600 s, so Q = 2 × 600 = 1200 C.
Remember

I = Q ÷ t; 1 A = 1 C/s; e = 1.6 × 10⁻¹⁹ C. Free electrons carry current in metals.

Common mistake

Using minutes directly in I = Q ÷ t. Always convert time to seconds.

Shortcut

Memory clue: "Current = Charge per second"; 1 ampere = 1 coulomb per second.

Spot the difference

QuantitySymbolUnit
ChargeQCoulomb (C)
CurrentIAmpere (A)
TimetSecond (s)

Practice questions

Easy
  1. 1What is electric current?
  2. 2What carries current in metals?
  3. 3What is the SI unit of current?
Medium
  1. 4What is the charge of an electron?
  2. 5Find the current if 30 C flows in 10 s.
  3. 6How much charge flows in 2 minutes when the current is 0.5 A?
Challenging
  1. 7How many electrons make up 1.6 C?
  2. 8Why is the direction of conventional current opposite to the direction of electron flow?
Show answers (try them yourself first)
  1. 1The rate of flow of charge.
  2. 2Free electrons.
  3. 3Ampere (1 A = 1 C/s)
  4. 41.6 × 10⁻¹⁹ C
  5. 530 ÷ 10 = 3 A
  6. 60.5 × 120 = 60 C
  7. 71.6 ÷ (1.6 × 10⁻¹⁹) = 10¹⁹ electrons
  8. 8Early scientists assumed positive charges flow; electrons, which are negative, actually flow the other way.

Ohm's law and resistance

From daily life

A narrow lane makes a crowd move slowly, and a wide road lets it move fast. In a wire, how much it opposes the flow of current is called resistance. A thin, long wire resists more than a thick, short one.

Simple definition

Ohm's law (ओहमचा नियम): V = I × R. Resistance (रोध) R opposes the flow of current.

A straight line through the origin showing voltage proportional to current with slope 5 ohms12345101520xyOhm's law: V against I for a 5 Ω resistorV = I Rslope = V/I = 15/3 = 5 ΩI (A)

In the figure : In the figure Ohm's law: V is proportional to I, and the slope is the resistance.

Rule 1: Ohm's law — V = I × R at constant temperature. The unit of resistance is the ohm (Ω). The graph of V against I is a straight line and its slope is R. An ammeter is connected in series and a voltmeter in parallel.

  • Easy : V = 12 V, R = 4 Ω: I = V ÷ R = 12 ÷ 4 = 3 A.
  • Medium : I = 0.5 A, R = 20 Ω: V = 0.5 × 20 = 10 V.
  • Exam-type : A graph of V against I passes through (0.2 A, 1 V) and (0.4 A, 2 V): slope = 1 ÷ 0.2 = 5 Ω.
Live figure

Ohm's law and resistance

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Live figure

Ohm's law and resistance

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Rule 2: Resistivity — R = ρL ÷ A, where ρ is the resistivity (विशिष्ट रोध), L the length and A the cross-section area. The unit of resistivity is Ω m. Copper 1.7 × 10−8 Ω m; nichrome 1.1 × 10−6 Ω m. Conductors have low resistance and insulators have very high resistance.

  • Easy : A longer wire has more resistance; a thicker wire has less.
  • Medium : A copper wire L = 10 m, A = 1 mm² = 10⁻⁶ m²: R = 1.7 × 10⁻⁸ × 10 ÷ 10⁻⁶ = 0.17 Ω.
  • Exam-type : A nichrome wire with L = 2 m and A = 10⁻⁶ m²: R = 1.1 × 10⁻⁶ × 2 ÷ 10⁻⁶ = 2.2 Ω. It resists about 13 times more than copper of the same size.
Remember

V = IR. R = ρL ÷ A. Ammeter in series, voltmeter in parallel.

Common mistake

Connecting a voltmeter in series. A voltmeter is connected in parallel.

Shortcut

Memory clue: "Ammeter = Alone in line (series); Voltmeter = Via both ends (parallel)".

Spot the difference

QuantityFormulaUnit
Ohm's lawV = IRV
ResistanceR = V ÷ IΩ
Resistivityρ = RA ÷ LΩ m

Practice questions

Easy
  1. 1State Ohm's law.
  2. 2What is the unit of resistance?
  3. 3What does the slope of a V–I graph give?
Medium
  1. 4How are an ammeter and a voltmeter connected?
  2. 5Find I when V = 24 V and R = 6 Ω.
  3. 6Find R if 2 A flows when the potential difference is 10 V.
Challenging
  1. 7A wire has R = 8 Ω. If its length is doubled at the same thickness, what is the new R?
  2. 8Why are heater coils made of nichrome and not copper?
Show answers (try them yourself first)
  1. 1At constant temperature the current through a conductor is proportional to the potential difference across it, V = IR.
  2. 2Ohm (Ω)
  3. 3The resistance.
  4. 4Ammeter in series; voltmeter in parallel.
  5. 524 ÷ 6 = 4 A
  6. 610 ÷ 2 = 5 Ω
  7. 7R ∝ L, so 16 Ω.
  8. 8Nichrome has a much higher resistivity (1.1 × 10⁻⁶ vs 1.7 × 10⁻⁸ Ω m), so it gives more heat for the same current.

Series and parallel resistors

From daily life

Fairy lights on a string: in some old strings, when one bulb is removed the whole string goes dark. In a house, if one tube light fails, the fan still runs. The first is a series arrangement and the second is a parallel arrangement.

Simple definition

In a series (श्रेणी) connection resistors are joined end to end. In a parallel (समांतर) connection they are joined across the same two points.

Two resistors of 2 and 3 ohms in series giving 5 ohms and in parallel giving 1.2 ohmsSeries: one path, same currentR₁ = 2 ΩR₂ = 3 ΩRs = 2 + 3 = 5 Ω (more than each)Parallel: two paths, same potential differenceR₁ = 2 ΩR₂ = 3 Ω1/Rp = 1/2 + 1/3 = 5/6, so Rp = 1.2 Ω (less than each)

In the figure : In the figure resistors in series add up; in parallel the total is smaller than each.

Rule 1: Series — The same current flows through every resistor. Rs = R₁ + R₂ + …. The total is larger than each. If one resistor fails, the circuit breaks.

  • Easy : 2 Ω + 3 Ω + 5 Ω in series: Rs = 10 Ω.
  • Medium : A 12 V cell on 2 Ω and 4 Ω in series: R = 6 Ω, I = 12 ÷ 6 = 2 A, and V across the 4 Ω is 2 × 4 = 8 V.
  • Exam-type : Voltages across the parts add up to the supply: 2 × 2 + 2 × 4 = 4 + 8 = 12 V.
Live figure

Series and parallel resistors

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Rule 2: Parallel — The potential difference across every resistor is the same. 1 ÷ Rp = 1 ÷ R₁ + 1 ÷ R₂ + …. The total is smaller than the smallest one. The currents add up.

  • Easy : 6 Ω and 3 Ω in parallel: 1/Rp = 1/6 + 1/3 = 3/6 = 1/2, so Rp = 2 Ω.
  • Medium : Two equal resistors of 10 Ω in parallel give 10 ÷ 2 = 5 Ω.
  • Exam-type : A 12 V supply on 6 Ω and 3 Ω in parallel: currents are 12 ÷ 6 = 2 A and 12 ÷ 3 = 4 A; the total current is 6 A, equal to 12 ÷ 2.
Live figure

Series and parallel resistors

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Remember

Series: same current, R adds. Parallel: same V, 1/R adds, total less than the smallest.

Common mistake

Adding resistances directly in parallel. Add the inverses, then invert the result.

Shortcut

Memory clue: "Series = Sum, Parallel = Pocket (smaller than the smallest)".

Spot the difference

PointSeriesParallel
CurrentSameSplits and adds
Potential differenceDividesSame
Total resistanceR₁ + R₂ + …1/R = 1/R₁ + 1/R₂ + …
If one failsCircuit breaksOthers work

Practice questions

Easy
  1. 1Which connection has the same current in all resistors?
  2. 2Which connection has the same potential difference across all resistors?
  3. 3Write the formula for resistors in series.
Medium
  1. 4Find R for 3 Ω, 4 Ω and 5 Ω in series.
  2. 5Find R for 4 Ω and 12 Ω in parallel.
  3. 6Three 6 Ω resistors are in parallel. Find the total.
Challenging
  1. 7A 9 V battery is joined to 3 Ω and 6 Ω in series. Find the current.
  2. 8Why are house appliances joined in parallel and not in series?
Show answers (try them yourself first)
  1. 1Series
  2. 2Parallel
  3. 3Rs = R₁ + R₂ + …
  4. 412 Ω
  5. 51/4 + 1/12 = 4/12 = 1/3, so 3 Ω.
  6. 66 ÷ 3 = 2 Ω
  7. 7R = 9 Ω; I = 9 ÷ 9 = 1 A
  8. 8Each gets the full voltage and works alone; if one is off or fails the others still work.

Domestic circuits, fuses and safety

From daily life

The iron box in a house is plugged into a socket marked with three holes. If a wire gets loose and touches the metal body, a person touching it could get a dangerous shock. Safety wires and fuses are there to protect us.

Simple definition

A fuse (फ्यूज) is a thin wire joined in series that melts when too much current flows, and so breaks the circuit.

Live, neutral and earth wires going to an appliance with a fuse in the live wireHouse wiring (about 220 V)FUSEAppliance(metal body)Live (red/brown)Neutral (blue/black)Earth (green/yellow)Fuse is in series: it melts if the current is too highAppliances are connected in parallelEarth wire carries stray current to the ground

In the figure : In the figure domestic wiring has a fuse and an earth wire.

Rule 1: Domestic circuit — Live (red or brown), neutral (blue or black) and earth (green or yellow) wires bring about 220 V into a house. Appliances are joined in parallel. A fuse is joined in series with the live wire and melts on excess current.

  • Easy : The supply is about 220 V and appliances are in parallel, so each gets 220 V.
  • Medium : A heater of 44 Ω on 220 V draws I = 220 ÷ 44 = 5 A.
  • Exam-type : An iron of 55 Ω draws 220 ÷ 55 = 4 A; a 5 A fuse allows it. A kettle of 22 Ω draws 220 ÷ 22 = 10 A, which melts a 5 A fuse.

Rule 2: Safety — Keep hands dry and wear rubber footwear when handling switches. Never touch a person who is getting a shock; switch off the main switch first.

  • Easy : Switch off the main switch before fixing a plug.
  • Medium : Earth wire: it carries leaked current safely to the ground, protecting a person touching the metal body.
  • Exam-type : If someone is stuck to a live wire, do not pull them with bare hands; switch off the main switch, or push them away with a dry wooden stick, and call for help (108).
Remember

Live, neutral, earth wires; 220 V; appliances in parallel; fuse in series melts on excess current.

Common mistake

Putting a thick copper wire instead of a fuse. It will not melt and the fire risk grows.

Shortcut

Memory clue: "Red = Risky (live), Green = Ground (earth)".

Spot the difference

WireColourJob
LiveRed or brownBrings current
NeutralBlue or blackReturns current
EarthGreen or yellowSafety

Practice questions

Easy
  1. 1What is the voltage of the domestic supply?
  2. 2Name the three wires in a domestic circuit and their colours.
  3. 3How is a fuse joined in a circuit?
Medium
  1. 4What does a fuse do on excess current?
  2. 5A heater of 22 Ω is on 220 V. Find the current.
  3. 6Will a 5 A fuse blow if a 55 Ω appliance is on 220 V?
Challenging
  1. 7Why is an earth wire given to an iron box?
  2. 8Give three safety rules to follow while using electricity.
Show answers (try them yourself first)
  1. 1About 220 V
  2. 2Live (red or brown), neutral (blue or black), earth (green or yellow).
  3. 3In series.
  4. 4It melts and breaks the circuit.
  5. 5220 ÷ 22 = 10 A
  6. 6No, I = 220 ÷ 55 = 4 A, which is below 5 A.
  7. 7To carry leaked current safely to the ground so the user does not get a shock.
  8. 8Keep hands dry, wear rubber footwear, switch off the main switch before repairs, and never touch a person getting a shock.

Quick revision

  • V = IR; I = Q/t; V = W/Q.
  • Series adds resistances; parallel adds inverses.