Electricity and Magnetism
🟢 Lite — Quick Review (1h–1d)
Rapid summary for last-minute revision.
Electric Current and Ohm’s Law
- Electric current (I): The flow of electric charge. Measured in Ampere (A). 1 A = 1 coulomb/second.
- Potential difference (V): The “push” that drives current through a conductor. Measured in Volts (V).
- Resistance (R): Opposition to the flow of current. Measured in Ohm (Ω).
Ohm’s Law: V = IR
This is the single most important formula in electricity for UPTET. It interlinks voltage, current, and resistance.
Example: A 12 V battery is connected to a resistor of 4 Ω. Current I = V/R = 12/4 = 3 A.
Series and Parallel Circuits
| Series Circuit | Parallel Circuit | |
|---|---|---|
| Current | Same through all components | Different through each branch |
| Voltage | Shared (V = V₁ + V₂ + …) | Same across all branches |
| Equivalent R | R = R₁ + R₂ + … | 1/R = 1/R₁ + 1/R₂ + … |
Series example: Three resistors 2 Ω, 3 Ω, 5 Ω in series → R = 10 Ω. Current from a 10 V source = 1 A.
Parallel example: Two resistors 6 Ω and 3 Ω in parallel → 1/R = 1/6 + 1/3 = ½ → R = 2 Ω.
Heating Effect of Current — Joule’s Law
When current flows through a conductor, it produces heat. This is the working principle of electric irons, heaters, and incandescent bulbs.
Joule’s Law: H = I²Rt
Where H = heat energy in joules, I = current in amperes, R = resistance in ohms, t = time in seconds.
Example: A current of 2 A flows through a 5 Ω resistor for 3 seconds. Heat produced = (2)² × 5 × 3 = 60 J.
Magnetic Effects
- A compass needle deflects when placed near a current-carrying wire.
- Magnetic field around a straight current-carrying conductor forms concentric circles.
- Right-hand thumb rule: If you point the thumb of your right hand in the direction of current, the curled fingers show the direction of the magnetic field.
Electromagnets: A solenoid (coil of wire) with a soft iron core becomes an electromagnet. Used in electric bells, cranes, and MRI machines.
⚡ Exam Tip: In UPTET, a frequent question type: “Calculate the total resistance of three 6 Ω resistors connected in series/parallel.” For parallel, 1/R = 1/6 + 1/6 + 1/6 = 3/6 = ½ → R = 2 Ω. For series, R = 18 Ω. Always check series vs parallel — they give dramatically different results.
⚡ Common Mistake: Confusing series and parallel current paths. In parallel, current splits but voltage is constant. In series, current is constant but voltage drops accumulate.
🟡 Standard — Regular Study (2d–2mo)
For students who want genuine understanding.
Electric Power and Energy
Power (P) is the rate at which electrical energy is used or transferred.
P = VI = I²R = V²/R
The unit of power is Watt (W). 1 kW = 1000 W.
Example: A 100 W bulb connected to 220 V draws current I = P/V = 100/220 ≈ 0.45 A. Resistance of the bulb = V²/P = 220²/100 = 484 Ω.
Electrical energy consumed = Power × time. Measured in kilowatt-hours (kWh). 1 kWh = 3.6 × 10⁶ J = 1 unit of electricity.
Example: A 1500 W geyser used for 2 hours. Energy = 1.5 × 2 = 3 kWh = 3 units.
Electricity bills in India are calculated in units (kWh). This is a very common UPTET question: “A 60 W fan runs for 10 hours. Calculate the cost at ₹ 5 per unit.”
Joule’s Law in Detail
The heating effect H = I²Rt is derived from:
- H = VIt (work done by voltage in moving charge)
- Using V = IR: H = I²Rt
The heating effect depends on:
- Current squared (I²): Doubling current quadruples heat (very significant).
- Resistance (R): Higher resistance produces more heat for the same current.
- Time (t): Longer duration produces more heat.
Practical applications of heating effect:
- Electric iron, toaster, heater, kettle
- Filament of incandescent bulb (tungsten, melting point 3422°C)
- Fuse wire (lead-tin alloy, low melting point ~183°C)
⚡ UPTET Common Mistakes:
- Mixing up kW and kWh. kW is power; kWh is energy. A 2 kW heater used for 3 hours consumes 6 kWh.
- Confusing Ohm’s law V = IR with P = VI — choose the right formula based on what’s asked.
- In parallel circuits, students forget that total current is the sum of branch currents.
- Forgetting that a battery’s internal resistance exists (though in simple problems we assume zero internal resistance).
Magnetic Field of a Solenoid
A solenoid is a coil of many turns of wire. When current passes through it, it behaves like a bar magnet.
- Magnetic field inside a solenoid is uniform (same strength at all points).
- Strength of magnetic field B ∝ number of turns (N) and current (I).
- B ∝ 1/length of solenoid (inversely proportional).
Right-Hand Thumb Rule: Thumb points in direction of current flow; curl of fingers shows direction of magnetic field lines around the conductor.
Applications of Electromagnetism:
- Electric bell: Electromagnet attracts the hammer; circuit breaks; hammer returns; cycle repeats.
- DC motor: Converts electrical energy to mechanical energy using magnetic effect on current-carrying conductor.
- Transformer: Changes AC voltage levels. Step-up (increases V, decreases I); Step-down (decreases V, increases I). Works only for AC.
Electric Motor
An electric motor works on the principle: a current-carrying conductor placed in a magnetic field experiences a force. Force F = BIL (B = magnetic field strength, I = current, L = length of conductor). The direction is given by Fleming’s left-hand rule.
Generator (Dynamo)
Works on the principle of electromagnetic induction: a rotating coil in a magnetic field induces electric current. Mechanical energy → Electrical energy. This is the reverse of a motor.
Electromagnetic Induction (Faraday’s Law):
- Induced EMF is proportional to the rate of change of magnetic flux.
- The direction of induced current is given by Lenz’s Law (opposes the cause).
⚡ UPTET Question Pattern: Questions on electromagnetic induction usually ask: “What is the direction of induced current?” Apply Lenz’s law — induced current flows in a direction that opposes the change in magnetic flux.
Domestic Electric Circuits
In India, household circuits use:
- Live wire (Red): 220 V, carries current.
- Neutral wire (Black): Returns current.
- Earth wire (Green): Safety measure.
Fuse rating (in amperes) is chosen based on the maximum current the circuit can carry. A 5 A fuse for a 1000 W appliance at 220 V (since I = 1000/220 ≈ 4.5 A).
🔴 Extended — Deep Study (3mo+)
Comprehensive theory for students with extended preparation time.
Series and Parallel — Detailed Analysis
Series circuit analysis:
- Current is the same through every component (conservation of charge).
- Total voltage = sum of individual voltages (V = V₁ + V₂ + …).
- Total resistance = sum of individual resistances (R = R₁ + R₂ + …).
- If one component fails (burns out), the entire circuit breaks.
Parallel circuit analysis:
- Voltage is the same across each parallel branch.
- Total current = sum of currents in each branch (I = I₁ + I₂ + …).
- Total resistance: For two resistors in parallel R = (R₁R₂)/(R₁ + R₂).
- If one branch fails, current continues in other branches.
Special case: n identical resistors R connected in parallel → R_eq = R/n.
Combined circuits (series + parallel) are solved by reducing step by step. Identify which resistors are in series and which are in parallel, then reduce iteratively.
Magnetic Effects of Current — Full Treatment
Biot-Savart Law (not required for UPTET but useful for conceptual depth): Magnetic field at a point due to a current element is proportional to (I × dl × sinθ)/r².
Magnetic field due to a straight conductor: B ∝ I/(2πr) where r is the perpendicular distance from the conductor.
Right-hand thumb rule (with illustration):
- Point thumb along the wire in the direction of current.
- Curl fingers — the fingers show the circular magnetic field lines.
- In the region above the wire, field points one direction; below the wire, the opposite.
Force on a Current-Carrying Conductor in a Magnetic Field
Fleming’s Left-Hand Rule:
- Hold thumb, forefinger, and middle finger of your LEFT hand at right angles.
- Forefinger → direction of magnetic field (N to S).
- Middle finger → direction of current (positive to negative).
- Thumb → direction of force/motion.
Force F = BIL sinθ. If conductor is parallel to the field (θ=0°), force = 0. If perpendicular (θ=90°), F = BIL (maximum).
Electric Motor (Detailed):
A rectangular coil ABCD carrying current is placed between the poles of a magnet.
- Side AB and CD experience forces — one upward, one downward (by Fleming’s left-hand rule).
- These two forces form a torque that rotates the coil.
- Commutator (split ring) reverses the direction of current every half rotation to maintain continuous rotation.
- In a DC motor, the commutator ensures the coil always rotates in the same direction.
Electromagnetic Induction (Faraday’s Laws):
- An EMF is induced in a coil when magnetic flux through the coil changes.
- Magnitude of induced EMF ∝ rate of change of magnetic flux.
- Direction of induced current given by Lenz’s Law: induced current opposes the change in magnetic flux.
Lenz’s Law example: If you push a magnet into a coil, the coil’s induced current creates its own magnetic field that opposes the incoming magnet (repels it). Pull the magnet out → induced current reverses direction (attracts the magnet). The coil always “fights” the change.
AC Generator:
- Rotating coil in a magnetic field generates alternating current (AC).
- Frequency = 50 Hz in India (direction changes 100 times per second).
- Output voltage V = V₀ sin ωt where V₀ = peak voltage, ω = angular frequency.
- In India, V₀ ≈ 310 V (since V_rms = 220 V, and V₀ = √2 × V_rms).
Transformer:
- Works on electromagnetic induction — only for AC.
- Step-up: Ns > Np → Vs > Vp (voltage increases, current decreases).
- Step-down: Ns < Np → Vs < Vp.
- Power input ≈ Power output (ideal transformer): Vp × Ip = Vs × Is.
- If voltage increases 10×, current decreases 10× (for same power).
⚡ Previous Year UPTET Focus: Questions on domestic wiring, fuse selection, and calculation of electricity bills appear almost every year. Expect a numerical like: “A 1000 W microwave oven is used 30 minutes daily at ₹ 6 per unit. Find the monthly electricity cost.” Answer: 0.5 kWh × 30 days = 15 kWh × ₹ 6 = ₹ 90.
⚡ Key Formula Summary for Quick Revision:
- V = IR (Ohm’s law)
- P = VI = I²R = V²/R
- H = I²Rt (Joule’s heating)
- F = BIL sinθ (force on conductor in magnetic field)
- Vp/Vs = Np/Ns (transformer)
⚡ Common Errors to Flag:
- In parallel, the formula for equivalent resistance of two resistors R = (R₁R₂)/(R₁+R₂) — do not invert accidentally.
- Confusion between direction of current (conventionally positive to negative) and electron flow (negative to positive).
- Forgetting that the heating effect depends on I², not I — doubling current quadruples heat, not doubles.
- Assuming electromagnets are permanent — they can be turned on/off, unlike permanent magnets.