Physical Science Classes VI-X for School Assistants and TET Paper 2A · Chapter 6

Electricity, Circuits, Power; Magnetism and Electromagnetism

What to remember

Current I = Q/t (ampere), potential difference V = W/Q (volt), and Ohm's law V = IR (resistance in ohm). Resistances add in series; in parallel the reciprocals add. Power P = VI = I²R = V²/R.
Kirchhoff's current law: the total current entering a junction equals the total leaving. Kirchhoff's voltage law: the algebraic sum of potential changes around a closed loop is zero.
A current produces a magnetic field (Oersted). A conductor carrying current in a magnetic field feels a force (motor, Fleming's left-hand rule); a changing magnetic flux produces an EMF (generator, Fleming's right-hand rule).

Charge, current and potential difference

Electric charge is measured in coulomb (C). The charge of one electron is about 1.6 x 10⁻¹⁹ C, so 1 C is the charge of about 6.25 x 10¹⁸ electrons. Like charges repel; unlike charges attract.

Current: rate of flow of charge, I = Q / t. Unit: ampere (A) = 1 coulomb per second. By convention, current flows from the positive terminal to the negative terminal outside the cell, opposite to the movement of electrons. It is measured by an ammeter, connected in series.
Potential difference: work done per unit charge, V = W / Q. Unit: volt (V) = 1 joule per coulomb. Measured by a voltmeter, connected in parallel across the component.
EMF of a cell is its potential difference when no current is drawn. A cell with EMF E and internal resistance r supplying an external resistance R gives I = E / (R + r).

Ohm's law and resistance

Ohm's law: at constant temperature, the current through a conductor is proportional to the potential difference across it: V = I R. Resistance R is measured in ohm (Ω). The V-I graph of an ohmic conductor is a straight line through the origin.

Resistivity: R = ρ L / A, where L is length and A is area of cross-section. Resistance increases with length and decreases with area; doubling the diameter reduces the resistance to one-fourth. Resistivity ρ depends on the material and temperature, not on the shape (unit Ω m). Metals have low resistivity; alloys (nichrome, manganin, constantan) have higher resistivity and change little with temperature. Resistance of metals rises with temperature.

Conductors: metals, graphite. Insulators: rubber, glass, dry wood, plastic. Tungsten (high melting point) is used for bulb filaments; nichrome for heating elements.

Series and parallel combinations

Property	Series	Parallel
Current	Same in all	Divides between branches
Potential difference	Divides	Same across all
Equivalent resistance	R = R₁ + R₂ + R₃	1/R = 1/R₁ + 1/R₂ + 1/R₃
Effect	Total R is larger than the largest	Total R is smaller than the smallest
If one device fails	Whole circuit breaks	Others keep working

Household appliances are connected in parallel so that each gets the full mains voltage and works independently.

Worked example 1: 2 Ω, 3 Ω and 5 Ω in series give 10 Ω. A 20 V supply gives I = 2 A.

Worked example 2: 6 Ω and 3 Ω in parallel: 1/R = 1/6 + 1/3 = 1/2, so R = 2 Ω. For two resistors, R = (R₁R₂)/(R₁ + R₂) = 18/9 = 2 Ω.

Kirchhoff's laws

Junction (current) law: at any junction, the sum of the currents entering equals the sum of the currents leaving. This is the conservation of charge.
Loop (voltage) law: around any closed loop, the algebraic sum of the EMFs equals the algebraic sum of the potential drops (I R). This is the conservation of energy.

Example: 3 A and 2 A enter a junction, and 1 A leaves in one wire. The current in the other wire is 4 A.

Heating effect, power and domestic circuits

Joule's law of heating: H = I² R t. Used in the electric heater, iron, geyser, toaster and bulb. The fuse is a wire of low melting point connected in series; it melts when the current is too high and protects the appliances. Choose a fuse rated a little above the normal current (a 1 kW appliance on 220 V draws about 4.5 A, so a 5 A fuse is suitable).

Electric power: P = VI = I²R = V²/R; unit watt. Energy in kWh = power (kW) x time (hours). A 100 W bulb used for 10 hours uses 1 kWh (one unit).

Worked example 3: heat in a 5 Ω resistor carrying 2 A for 10 s = 2² x 5 x 10 = 200 J.

Worked example 4: a 100 W bulb on 220 V has resistance V²/P = 220²/100 = 484 Ω.

Domestic wiring: mains supply in India is about 220 V AC at 50 Hz. Three wires: live (phase), neutral and earth. The live wire carries current and has the fuse and switch; the earth wire connects the metal body of the appliance to the ground and prevents shock. Short circuit occurs when live and neutral touch and the current becomes very large; overloading is too many appliances on one circuit. An MCB (miniature circuit breaker) now replaces the fuse in many homes.

Magnetism

A magnet has two poles, north and south; like poles repel and unlike poles attract. A freely suspended magnet points north-south. A magnet cannot be broken into separate single poles.

Magnetic field lines run outside the magnet from north to south and inside from south to north. They form closed curves, never cross, and are closer together where the field is stronger. The Earth behaves as a large bar magnet.

Magnetic materials: iron, cobalt, nickel (ferromagnetic). Soft iron is used for temporary magnets and electromagnets; steel for permanent magnets.

Electromagnetism

Oersted's experiment: a current-carrying wire deflects a nearby compass needle, showing that a current produces a magnetic field. The field around a straight wire is in concentric circles; its direction is given by the right-hand thumb rule (thumb along the current, curled fingers show the field). Stronger current gives a stronger field and the field is weaker with distance.

A solenoid (coil of many turns) has a field like a bar magnet: uniform inside, with a north and south end. An electromagnet is a soft iron core inside a solenoid; its strength depends on the number of turns, the current, and the core. It is used in electric bells, cranes for lifting scrap, and relays.

Force on a current-carrying conductor: a conductor in a magnetic field experiences a force, which is greatest when the current is at right angles to the field. Fleming's left-hand rule: thumb, forefinger and middle finger mutually perpendicular: forefinger = field, middle finger = current, thumb = force (motion). This is the working principle of the electric motor, which converts electrical energy into mechanical energy; its parts include armature coil, split-ring commutator, brushes and magnets.

Electromagnetic induction (Faraday): a changing magnetic flux through a coil induces an EMF and a current. Lenz's law: the induced current opposes the change that produced it. Fleming's right-hand rule gives the direction of the induced current (forefinger = field, thumb = motion, middle finger = current). This is the principle of the generator (dynamo), which converts mechanical energy into electrical energy. An AC generator uses slip rings; a DC generator uses a split-ring commutator.

A transformer works on mutual induction and only with AC. Vs/Vp = Ns/Np. A step-up transformer has more turns in the secondary and increases the voltage; a step-down transformer has fewer. Power is transmitted at high voltage to reduce loss (I²R).

Classroom angle

Verify Ohm's law with a cell, a nichrome wire, an ammeter and a voltmeter; plot V against I and show a straight line.
Sprinkle iron filings on a card over a bar magnet and tap it gently to show the field-line pattern.
Move a bar magnet in and out of a coil connected to a galvanometer; the needle deflects only while the magnet moves, showing induction.
Keep safety rules clear for pupils: never touch bare mains wires, never use wet hands on a switch, and always use a plug with earth.

Exam traps

The ammeter is in series and the voltmeter is in parallel.
The direction of conventional current is opposite to the flow of electrons.
Resistivity does not depend on length or area; resistance does.
Parallel resistance is smaller than the smallest resistor.
The kilowatt-hour is a unit of energy, not power.
The fuse goes in the live wire, in series.
A motor uses the left-hand rule; a generator uses the right-hand rule.
A transformer does not work on DC.
Magnetic field lines are closed loops, from N to S outside the magnet.

One-liners

1. Unit of current is the ampere; of potential difference the volt; of resistance the ohm.
2. V = I R.
3. R = ρ L / A.
4. Series: R = R₁ + R₂.
5. P = V I.
6. 1 kWh = 3.6 x 10⁶ J.
7. Fuse wire has a low melting point.
8. Mains supply in India is 220 V, 50 Hz AC.
9. Oersted showed that a current produces a magnetic field.
10. Faraday discovered electromagnetic induction.
11. A motor converts electrical energy into mechanical energy.
12. A generator converts mechanical energy into electrical energy.

Practice questions

The SI unit of electric current is
1. volt
2. ohm
3. coulomb
4. ampere
Answer
D. ampere
Current is charge per second; 1 A = 1 C/s.
An ammeter is connected in a circuit
1. in parallel
2. across the battery only
3. in any way
4. in series
Answer
D. in series
It must carry the whole circuit current and has very low resistance.
A voltmeter is connected
1. in series
2. after the switch only
3. in parallel across the component
4. in the earth wire
Answer
C. in parallel across the component
It measures the potential difference across the component.
The SI unit of potential difference is
1. tesla
2. volt
3. watt
4. ampere
Answer
B. volt
1 V = 1 J/C.
According to Ohm's law, at constant temperature the current through a conductor is
1. inversely proportional to the potential difference
2. proportional to the resistance
3. independent of the potential difference
4. proportional to the potential difference
Answer
D. proportional to the potential difference
V = I R, so I is proportional to V.
The resistance of a uniform wire is inversely proportional to its
1. length
2. area of cross-section
3. temperature in kelvin
4. resistivity
Answer
B. area of cross-section
R = rho L / A, so R varies as 1/A.
The unit of resistivity is
1. ohm per metre
2. ohm
3. ohm metre
4. siemens
Answer
C. ohm metre
From rho = R A / L, the unit is ohm x m^2 / m = ohm metre.
Household appliances are connected in parallel so that
1. the current is the same in all
2. less electricity is used
3. the total resistance is large
4. each gets the full voltage and works independently
Answer
D. each gets the full voltage and works independently
In parallel the potential difference is the same across each branch.
The fuse wire has
1. zero resistance
2. a low melting point
3. a very large diameter
4. a high melting point
Answer
B. a low melting point
It melts when the current becomes too high and breaks the circuit.
The earth wire in domestic wiring is connected to
1. the switch only
2. the metal body of the appliance
3. the fuse only
4. the neutral at the bulb
Answer
B. the metal body of the appliance
It gives the leakage current a safe path to the ground.
The mains supply voltage and frequency used in India are
1. 220 V and 50 Hz
2. 110 V and 60 Hz
3. 440 V and 50 Hz
4. 220 V and 100 Hz
Answer
A. 220 V and 50 Hz
Domestic supply is about 220 V AC at 50 Hz.
Oersted's experiment showed that
1. charge is quantised
2. light is a wave
3. a magnet produces current
4. a current produces a magnetic field
Answer
D. a current produces a magnetic field
A compass needle deflects near a current-carrying wire.
Fleming's left-hand rule gives the direction of
1. magnetic field of a magnet
2. induced current
3. force on a current-carrying conductor in a magnetic field
4. charge on a body
Answer
C. force on a current-carrying conductor in a magnetic field
Forefinger field, middle finger current, thumb force.
An electric generator converts
1. chemical energy into mechanical energy
2. electrical energy into mechanical energy
3. mechanical energy into electrical energy
4. heat into light
Answer
C. mechanical energy into electrical energy
It works on electromagnetic induction.
A transformer works on
1. DC only
2. mutual induction with AC
3. static electricity
4. Oersted's effect
Answer
B. mutual induction with AC
A changing flux in the primary induces an EMF in the secondary; DC gives no change of flux.
The material used for the filament of an electric bulb is
1. aluminium
2. nichrome
3. copper
4. tungsten
Answer
D. tungsten
Tungsten has a very high melting point.
The three resistors 2 ohm, 3 ohm and 5 ohm are connected in series. The equivalent resistance is
1. 10 ohm
2. 0.97 ohm
3. 1 ohm
4. 30 ohm
Answer
A. 10 ohm
Series: 2 + 3 + 5 = 10 ohm.
Resistors of 6 ohm and 3 ohm are connected in parallel. The equivalent resistance is
1. 4.5 ohm
2. 9 ohm
3. 2 ohm
4. 18 ohm
Answer
C. 2 ohm
(6 x 3)/(6 + 3) = 2 ohm.
The current through a 4 ohm resistor connected to a 12 V battery is
1. 0.33 A
2. 48 A
3. 8 A
4. 3 A
Answer
D. 3 A
I = V / R = 12 / 4 = 3 A.
A current of 2 A flows for 10 s. The charge that passes is
1. 20 C
2. 5 C
3. 0.2 C
4. 12 C
Answer
A. 20 C
Q = I t = 2 x 10 = 20 C.
The power of an appliance drawing 5 A at 220 V is
1. 1100 W
2. 44 W
3. 225 W
4. 4400 W
Answer
A. 1100 W
P = V I = 220 x 5 = 1100 W.
A 100 W bulb is used for 10 hours. The energy consumed is
1. 100 kWh
2. 10 kWh
3. 0.1 kWh
4. 1 kWh
Answer
D. 1 kWh
100 W x 10 h = 1000 Wh = 1 kWh.
The heat produced in a 5 ohm resistor carrying 2 A for 10 s is
1. 50 J
2. 200 J
3. 20 J
4. 100 J
Answer
B. 200 J
H = I^2 R t = 4 x 5 x 10 = 200 J.
The resistance of a 100 W, 220 V bulb is
1. 48.4 ohm
2. 2.2 ohm
3. 484 ohm
4. 22000 ohm
Answer
C. 484 ohm
R = V^2 / P = 48400 / 100 = 484 ohm.
The length of a wire is doubled with its area of cross-section unchanged. Its resistance becomes
1. double
2. four times
3. half
4. unchanged
Answer
A. double
R is proportional to length, so it doubles.
The diameter of a wire is doubled with its length unchanged. Its resistance becomes
1. four times
2. half
3. one-fourth
4. double
Answer
C. one-fourth
Area becomes four times, so R becomes one-fourth.
At a junction, 3 A and 2 A enter, and 1 A leaves in one wire. The current in the other outgoing wire is
1. 6 A
2. 4 A
3. 2 A
4. 1 A
Answer
B. 4 A
Kirchhoff: current in = current out; 5 = 1 + x, so x = 4 A.
Two 4 ohm resistors are connected in parallel across a 4 V battery. The total current drawn is
1. 1 A
2. 4 A
3. 0.5 A
4. 2 A
Answer
D. 2 A
Equivalent R = 2 ohm; I = 4 / 2 = 2 A.
The work done in moving a charge of 2 C through a potential difference of 12 V is
1. 24 J
2. 6 J
3. 0.17 J
4. 14 J
Answer
A. 24 J
W = Q V = 2 x 12 = 24 J.
A cell of EMF 12 V and internal resistance 1 ohm is connected to an external resistance of 5 ohm. The current is
1. 3 A
2. 12 A
3. 2 A
4. 2.4 A
Answer
C. 2 A
I = E / (R + r) = 12 / 6 = 2 A.
Which of the following is a ferromagnetic material?
1. Glass
2. Wood
3. Copper
4. Iron
Answer
D. Iron
Iron, cobalt and nickel are strongly attracted by a magnet.
A step-up transformer has 100 turns in the primary and 1000 turns in the secondary. If the input is 220 V, the output voltage is
1. 1100 V
2. 2200 V
3. 22 V
4. 220 V
Answer
B. 2200 V
Vs = Vp x Ns/Np = 220 x 10 = 2200 V.
A 1 kW heater runs on a 220 V supply. The most suitable fuse rating is
1. 20 A
2. 5 A
3. 1 A
4. 0.5 A
Answer
B. 5 A
I = 1000/220 = about 4.5 A, so a 5 A fuse.
Power is transmitted at high voltage to reduce loss because the loss is
1. independent of the current
2. proportional to the voltage
3. V^2 R
4. I^2 R, and a higher voltage means a lower current
Answer
D. I^2 R, and a higher voltage means a lower current
For a fixed power P = V I, a larger V gives a smaller I and so smaller I^2 R loss.
Magnetic field lines
1. form closed loops, from N to S outside the magnet
2. are straight lines everywhere
3. cross each other near the poles
4. begin at the south pole and end at the north pole outside the magnet
Answer
A. form closed loops, from N to S outside the magnet
Outside the magnet the direction is from N to S and inside from S to N.
The core of an electromagnet is made of soft iron because it
1. is a permanent magnet
2. is easily magnetised and demagnetised
3. has high resistance
4. is cheap and light only
Answer
B. is easily magnetised and demagnetised
Soft iron loses its magnetism when the current is switched off.
When a bar magnet is moved in and out of a coil, the galvanometer deflects because
1. the magnet heats the wire
2. the coil becomes hot
3. a changing magnetic flux induces an EMF
4. the magnet gives its charge
Answer
C. a changing magnetic flux induces an EMF
This is electromagnetic induction.
Which of the statements is/are correct? 1. Conventional current flows from the positive to the negative terminal outside the cell. 2. Electrons flow in the same direction as conventional current.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Electrons flow opposite to the conventional current.
Which of the statements is/are correct? 1. In a parallel circuit the potential difference across each branch is the same. 2. In a series circuit the current is different in each resistor.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
The current is the same in a series circuit.
Which of the statements is/are correct? 1. An electric motor works on Fleming's left-hand rule. 2. A generator works on electromagnetic induction.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
Both are correct.
Which of the statements is/are correct? 1. A transformer can step up a DC voltage. 2. A fuse is connected in series in the live wire.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
A transformer needs a changing flux, hence AC.
Which of the statements is/are correct? 1. Kirchhoff's current law is based on conservation of charge. 2. Kirchhoff's voltage law is based on conservation of energy.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
Both are correct.
Which of the statements is/are correct? 1. The resistivity of a material depends on its length. 2. A kilowatt-hour is a unit of power.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
D. Neither 1 nor 2
Resistivity is a material property; kWh is a unit of energy.
Which of the pairs is correctly matched?
1. Ammeter - parallel
2. Solenoid - no magnetic field
3. Dynamo - electric motor principle
4. Fuse - low melting point wire
Answer
D. Fuse - low melting point wire
An ammeter is in series; a solenoid has a field like a bar magnet; a dynamo uses induction.
Which of the statements is/are correct? 1. The magnetic field of a straight current-carrying wire is in concentric circles around it. 2. The field becomes weaker with distance from the wire.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
Both are correct.

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1.The charge of two H + ions is ________.
2.The charge flowing through a circuit in 10 minutes is 300 C. Find the current drawn by the circuit.
3.The correct relation between charge(Q) following through a conductor, time(t) for which the charge follows and the current (I) following through the conductor is:
4.The formula of current I = _______ /time (t).
5.The generation of heat in a conductor due to electric current is known as:
6.The effective resistance of the parallel combination of two resistors is always _______
7.The electric dipole moment per unit volume is called ___________.
8.The electric current flowing through a metallic wire is directly proportional to the potential difference V across its ends, provided its _____ remains the same.
9.The electric ______ between two points in an electric circuit carrying some current is the work done to move a unit charge from one point to the other.
10.The electric power consumed by a resistor of resistance R, carrying current I, is _______

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