Electric Current & Magnetic Effects: Formulas, Diagrams, MCQs

Electricity runs almost everything around us – lights, fans, mobile phones, trains and hospitals. At its heart is a simple idea: when electric charges flow through a wire, they make an electric current. And whenever a current flows, it also creates a magnetic field around it. This deep link between electricity and magnetism gives us electric motors, generators, transformers, electric bells, MRI machines and even magnetic levitation (maglev) trains.

Electricity and magnetism form one of the most important parts of General Science in SSC, Railways (RRB NTPC, Group D, ALP, JE), WBCS, Police and State PSC exams. Questions are asked on units, formulas, Ohm's law, series and parallel circuits, heating effect, electric power and bills, Fleming's rules, motors, generators, transformers and household wiring. This guide explains everything in simple language with clear diagrams, solved numerical examples, a formula sheet, a quick revision box with memory tricks and 20 MCQs with answers.

➤ Electric current: I = Q/t · SI unit ampere (A)
➤ Ohm's law: V = IR · Resistance unit ohm (Ω)
➤ Electric power: P = VI = I²R = V²/R · 1 kWh = 3.6 × 10⁶ J
➤ Heating effect: H = I²Rt (Joule's law)
➤ Magnetic effect: Discovered by Oersted (1820) · Fleming's left-hand rule for motors, right-hand rule for generators
➤ Domestic supply in India: AC, about 220–230 V, 50 Hz

Part A: Electric Charge – The Starting Point

• Electric charge is a basic property of matter. There are two types: positive (carried by protons) and negative (carried by electrons)
• Like charges repel, unlike charges attract
• SI unit of charge: coulomb (C)
• Charge of one electron: e = 1.6 × 10⁻¹⁹ C (negative). So 1 coulomb ≈ 6.25 × 10¹⁸ electrons
• Charge is quantised (Q = ne, where n is a whole number) and conserved (it can neither be created nor destroyed)

Part B: Electric Current, Potential Difference and Circuits

Electric Current

Electric current is the rate of flow of electric charge through a conductor.

I = Q / t

• I = current, Q = charge, t = time
• SI unit: ampere (A). 1 ampere = 1 coulomb per second. Smaller units: milliampere (1 mA = 10⁻³ A), microampere (1 μA = 10⁻⁶ A)
• Current is measured by an ammeter, always connected in series. An ideal ammeter has zero resistance
• Conventional current flows from the positive terminal to the negative terminal. Electrons actually move in the opposite direction (negative to positive)
• Current is a scalar quantity, even though it has a direction

Example: A charge of 30 C flows through a bulb in 1 minute. Current I = Q/t = 30 C ÷ 60 s = 0.5 A.

Potential Difference (Voltage)

Charges flow only when there is a potential difference between two points – just as water flows from a higher level to a lower level. It is the work done to move a unit charge from one point to another.

V = W / Q

• SI unit: volt (V). 1 volt = 1 joule per coulomb
• Measured by a voltmeter, always connected in parallel. An ideal voltmeter has infinite resistance
• A cell or battery provides the potential difference. A single dry cell gives about 1.5 V
• The volt is named after Alessandro Volta, who invented the first battery (the Voltaic pile) in 1800

Electric Circuit and Symbols

A closed, continuous path for current is called an electric circuit. If the path is broken (switch OFF), it is an open circuit and no current flows.

Figure 1: A simple electric circuit – the ammeter is in series and the voltmeter is in parallel across the bulb.

Part C: Ohm's Law and Resistance

Ohm's Law

Stated by German physicist Georg Simon Ohm in 1827: at a constant temperature, the current through a conductor is directly proportional to the potential difference across its ends.

V ∝ I  ⇒  V = IR

Here R is the resistance – the property of a conductor that opposes the flow of current. Its SI unit is the ohm (Ω). 1 Ω = 1 V / 1 A.

Figure 2: V–I graph for a conductor obeying Ohm's law is a straight line through the origin; its slope gives the resistance.

Factors Affecting Resistance

R = ρ L / A

• Length (L): Resistance increases with length (R ∝ L). Doubling the length doubles the resistance
• Area of cross-section (A): Resistance decreases with thickness (R ∝ 1/A). A thick wire has less resistance
• Material: Depends on resistivity (ρ), whose SI unit is the ohm-metre (Ω m). Resistivity depends only on the material and temperature, not on the size of the wire
• Temperature: For metals, resistance increases with temperature. For semiconductors, it decreases

Example: A 10 Ω wire is stretched to double its length (its volume remains the same, so the area halves). New resistance = 10 × 2 × 2 = 40 Ω (R becomes 4 times).

Part D: Resistors in Series and Parallel

Figure 3: Resistors connected (a) in series and (b) in parallel.

Example: Three resistors of 6 Ω each. In series: Rs = 6 + 6 + 6 = 18 Ω. In parallel: 1/Rp = 1/6 + 1/6 + 1/6 = 3/6, so Rp = 2 Ω. Shortcut: n equal resistors R in parallel give R/n.

Why is household wiring parallel? Each appliance gets the full mains voltage, each can be switched on or off separately, and if one fails the rest keep working.

Part E: Heating Effect of Electric Current

When current flows through a resistor, part of the electrical energy changes into heat. Joule's law of heating states:

H = I²Rt

The heat produced is directly proportional to the square of the current, the resistance and the time. If the current doubles, the heat becomes four times.

Part F: Electric Power and Energy

Electric power is the rate at which electrical energy is used.

P = VI = I²R = V²/R

• SI unit of power: watt (W). 1 W = 1 V × 1 A. 1 kilowatt (kW) = 1000 W. 1 horsepower (hp) ≈ 746 W
• Electrical energy: E = P × t
• Commercial unit of energy: kilowatt-hour (kWh), also called 1 "unit" on your electricity bill
• 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J

Example – electricity bill: A 100 W bulb runs 10 hours daily for 30 days. Energy = 100 W × 10 h × 30 = 30,000 Wh = 30 kWh = 30 units. At ₹6 per unit, the cost is ₹180.

Example – current drawn: A 1100 W electric iron on a 220 V supply draws I = P/V = 1100/220 = 5 A. Its resistance is R = V²/P = 220²/1100 = 44 Ω.

AC and DC

Part G: Magnetic Effects of Electric Current

In 1820, Danish scientist Hans Christian Oersted noticed that a compass needle moved when current flowed in a nearby wire. This proved that electric current produces a magnetic field – the start of electromagnetism.

Magnet and Magnetic Field Lines

Figure 4: Magnetic field lines around a bar magnet.

• Outside a magnet, field lines go from the North pole to the South pole; inside, from South to North – so they form closed loops
• Field lines never cross each other (otherwise the field would have two directions at one point)
• Where lines are closer, the field is stronger (near the poles)
• SI unit of magnetic field (magnetic flux density): tesla (T); also gauss (1 T = 10⁴ gauss)
• Like poles repel, unlike poles attract. A freely suspended magnet points in the north–south direction

Magnetic Field Due to a Straight Current-Carrying Wire

The field lines are concentric circles around the wire. The field is stronger near the wire and with larger current.

Right-hand thumb rule (Maxwell's corkscrew rule): Hold the wire in your right hand with the thumb pointing in the direction of current; your curled fingers show the direction of the magnetic field.

Figure 5: Circular magnetic field lines around a straight wire carrying current out of the page.

Solenoid and Electromagnet

A solenoid is a long coil of many turns of insulated copper wire. When current flows, it behaves like a bar magnet, with a nearly uniform field inside. Placing a soft iron core inside makes a strong electromagnet.

Figure 6: A solenoid with a soft iron core works as an electromagnet.

Force on a Current-Carrying Conductor – Fleming's Left-Hand Rule

A wire carrying current in a magnetic field feels a force: F = BIL sin θ (maximum when the wire is perpendicular to the field). The direction is given by Fleming's left-hand rule: stretch the thumb, first finger and middle finger of your left hand at right angles to each other.

Figure 7: Fleming's left-hand rule – the three fingers are mutually perpendicular.

Application – Electric motor: Converts electrical energy into mechanical energy. A rectangular coil placed between magnet poles rotates when current flows. A split-ring commutator reverses the current every half turn so the coil keeps rotating in the same direction. Used in fans, mixers, washing machines, pumps, electric vehicles and trains.

Part H: Electromagnetic Induction

In 1831, Michael Faraday discovered that a changing magnetic field produces an electric current in a nearby coil. This is electromagnetic induction, and the current produced is the induced current.

• Moving a magnet into or out of a coil makes a galvanometer deflect; a stationary magnet produces no current
• Faster movement or more turns give a larger induced current
• Fleming's right-hand rule gives the direction of induced current: thumb = motion of conductor, first finger = field, middle finger = induced current
• Lenz's law: The induced current always opposes the change that produces it (a form of conservation of energy)

Electric Generator

A generator converts mechanical energy into electrical energy by rotating a coil in a magnetic field. An AC generator uses slip rings; a DC generator uses a split-ring commutator. Power stations – thermal, hydro, nuclear and wind – all use generators.

Transformer

Figure 8: A step-up transformer – the secondary coil has more turns than the primary.

Vs / Vp = Ns / Np

• Works on mutual induction and only with AC
• Step-up transformer (Ns > Np) increases voltage – used at power stations for long-distance transmission, because high voltage means low current and less heat loss
• Step-down transformer (Ns < Np) decreases voltage – used near homes and in mobile chargers
• Frequency does not change in a transformer

Example: A transformer has 100 turns in the primary and 2000 in the secondary. If Vp = 220 V, then Vs = 220 × 2000/100 = 4400 V (step-up).

Part I: Domestic Electric Circuits and Safety

• Earthing protects users from electric shocks from appliances with metal bodies (iron, refrigerator, geyser)
• Short circuit: Live and neutral wires touch directly; resistance becomes nearly zero and current becomes very large
• Overloading: Too many appliances on one socket or a sudden voltage rise
• Fuse and MCB (Miniature Circuit Breaker) cut off the supply automatically; they are always placed in the live wire. An MCB can be reset, while a fuse wire must be replaced
• Two separate circuits are used at home: about 5 A for lights and fans, and about 15 A for heavy appliances such as ACs, geysers and heaters

Types of Magnetic Materials

The Earth also behaves like a giant magnet. Its geographic North Pole is near the magnetic south pole of this imaginary magnet – that is why the north end of a compass needle points north.

Formula and Unit Sheet

Scientists Behind Electricity and Magnetism

Bengal connection: The Sidrapong Hydel Power Station near Darjeeling, started in 1897, is one of the earliest hydroelectric power stations in India, and Kolkata was among the first Indian cities to get a public electricity supply, through CESC, at the end of the 19th century.

Everyday Applications at a Glance

Engineering labs such as those of CSIR work on electric motors, sensors and electronic systems used in aircraft, while the satellites showcased in the new ISRO Space Gallery at Darbhanga run on solar cells that produce DC electricity. Indian-origin scientists working abroad in such fields are connected with Indian labs through the VAIBHAV Fellowship.

20 MCQs on Electric Current and Magnetic Effects

Q1. The SI unit of electric current is:
(a) Volt
(b) Ampere
(c) Coulomb
(d) Ohm

Answer: (b) – 1 ampere is a flow of 1 coulomb of charge per second.

Q2. The charge on one electron is:
(a) 1.6 × 10⁻¹⁹ C
(b) 9.1 × 10⁻³¹ C
(c) 1.6 × 10¹⁹ C
(d) 6.25 × 10¹⁸ C

Answer: (a) – 9.1 × 10⁻³¹ kg is the mass of an electron, a common trap.

Q3. An ammeter is always connected in a circuit:
(a) In parallel
(b) In series
(c) Either way
(d) Across the battery

Answer: (b) – A voltmeter is connected in parallel.

Q4. Ohm's law gives the relation between:
(a) Power and energy
(b) Current and potential difference
(c) Charge and time
(d) Resistance and temperature

Answer: (b) – V = IR at constant temperature.

Q5. The SI unit of resistivity is:
(a) Ohm
(b) Ohm per metre
(c) Ohm-metre
(d) Mho

Answer: (c) – Resistivity depends only on the material and temperature.

Q6. If the length of a wire is doubled by stretching, its resistance becomes:
(a) Half
(b) Double
(c) Four times
(d) Unchanged

Answer: (c) – Length doubles and area halves, so R = ρL/A becomes 4 times.

Q7. Three resistors of 9 Ω each are connected in parallel. The total resistance is:
(a) 27 Ω
(b) 9 Ω
(c) 3 Ω
(d) 1 Ω

Answer: (c) – For n equal resistors in parallel, R/n = 9/3 = 3 Ω.

Q8. Household appliances are connected in parallel because:
(a) It uses less wire
(b) Each appliance gets the same voltage and can work independently
(c) It increases total resistance
(d) It reduces the electricity bill

Answer: (b) – In series, one faulty appliance would stop all the others.

Q9. The heating element of an electric iron is made of:
(a) Copper
(b) Tungsten
(c) Nichrome
(d) Aluminium

Answer: (c) – Nichrome has high resistivity and does not oxidise easily.

Q10. The filament of an incandescent electric bulb is made of:
(a) Nichrome
(b) Tungsten
(c) Copper
(d) Silver

Answer: (b) – Tungsten has a very high melting point.

Q11. A fuse wire should have:
(a) High melting point
(b) Low melting point
(c) Zero resistance
(d) Infinite resistance

Answer: (b) – It is usually a tin–lead alloy and is placed in the live wire.

Q12. 1 kilowatt-hour is equal to:
(a) 3.6 × 10³ J
(b) 3.6 × 10⁵ J
(c) 3.6 × 10⁶ J
(d) 3.6 × 10⁹ J

Answer: (c) – 1000 W × 3600 s = 3,600,000 J.

Q13. An electric heater of 2000 W runs for 3 hours. The energy consumed is:
(a) 2 units
(b) 3 units
(c) 6 units
(d) 600 units

Answer: (c) – 2 kW × 3 h = 6 kWh = 6 units.

Q14. The frequency of AC household supply in India is:
(a) 50 Hz
(b) 60 Hz
(c) 100 Hz
(d) 220 Hz

Answer: (a) – The USA uses 60 Hz.

Q15. Who discovered that an electric current produces a magnetic field?
(a) Michael Faraday
(b) Hans Christian Oersted
(c) Georg Ohm
(d) James Maxwell

Answer: (b) – He observed a compass needle deflect near a current-carrying wire in 1820.

Q16. The SI unit of magnetic field is:
(a) Weber
(b) Gauss
(c) Tesla
(d) Henry

Answer: (c) – The weber is the unit of magnetic flux; the gauss is a non-SI unit.

Q17. The core of an electromagnet is made of:
(a) Steel
(b) Copper
(c) Soft iron
(d) Aluminium

Answer: (c) – Soft iron magnetises and demagnetises quickly; steel is used for permanent magnets.

Q18. Fleming's left-hand rule is used to find the direction of:
(a) Induced current in a generator
(b) Force on a current-carrying conductor in a motor
(c) Magnetic field around a straight wire
(d) Current in a transformer

Answer: (b) – The right-hand rule is used for generators.

Q19. Electromagnetic induction was discovered by:
(a) Nikola Tesla
(b) Thomas Edison
(c) Michael Faraday
(d) Alessandro Volta

Answer: (c) – He discovered it in 1831; it is the principle of generators and transformers.

Q20. A transformer works on:
(a) DC only
(b) AC only
(c) Both AC and DC
(d) Neither

Answer: (b) – It needs a changing magnetic field, which only AC provides.

Conclusion

Electric current and magnetism are two sides of the same coin – current produces magnetism, and changing magnetism produces current. These ideas power everything from a simple bulb to giant power stations. For exams, remember the units, the formulas (I = Q/t, V = IR, R = ρL/A, H = I²Rt, P = VI), series and parallel rules, the kWh conversion, Fleming's rules, and the working of motors, generators and transformers. Practise the solved examples and revise the memory tricks above before your exam.

Reference: NCERT Science Class X, Chapters "Electricity" and "Magnetic Effects of Electric Current"; NCERT Physics Class XII.