Chapter 4 — Electricity: Long Answer Questions
Ohm's Law
Statement: The current (I) flowing through a metallic conductor is directly proportional to the potential difference (V) across its ends, provided the temperature and other physical conditions remain constant.
Mathematical form:
Where R = resistance (constant for a given conductor at constant temperature). Unit: ohm (Ω).
Experiment to Verify Ohm's Law
Apparatus: Battery, rheostat (variable resistor), ammeter, voltmeter, resistor (R), connecting wires, key.
Circuit: Battery and rheostat connected in series with the resistor. Ammeter connected in series (to measure current). Voltmeter connected in parallel across the resistor (to measure voltage).
Procedure: 1. Close the key; adjust rheostat to get a small current I₁ 2. Note the current reading (I₁) and voltage reading (V₁) 3. Increase the rheostat setting to get I₂; note V₂ 4. Repeat for several different settings 5. Calculate V/I for each reading
Observation:
| V (volts) | I (amperes) | V/I (ohms) |
|---|---|---|
| 1.0 | 0.5 | 2.0 |
| 2.0 | 1.0 | 2.0 |
| 3.0 | 1.5 | 2.0 |
| 4.0 | 2.0 | 2.0 |
V/I = constant = R for all readings.
A graph of V vs I is a straight line through the origin — confirming Ohm's Law.
Conclusion: V/I = R = constant, verifying Ohm's Law.
Limitations of Ohm's Law
1. Not applicable to semiconductors: Diodes and transistors have non-linear I–V characteristics 2. Not applicable at high temperatures: Resistance of metals increases with temperature; the I–V relationship becomes non-linear 3. Not applicable to electrolytes: I–V relationship is non-linear 4. Not applicable to gas discharge tubes: Current does not follow Ohm's Law in ionised gases
Series Combination
Setup: Resistors R₁, R₂, R₃ connected end-to-end in a single path.
Key property: Same current (I) flows through all resistors.
Derivation:
- Voltage across R₁: V₁ = IR₁
- Voltage across R₂: V₂ = IR₂
- Voltage across R₃: V₃ = IR₃
- Total voltage: V = V₁ + V₂ + V₃ = IR₁ + IR₂ + IR₃ = I(R₁ + R₂ + R₃)
- But V = IR_equivalent
The equivalent resistance in series is the sum of all resistances. It is always greater than any individual resistance.
Applications of series circuits:
- Old decorative lights (if one bulb failed, all went out — a disadvantage)
- Fuse wires (in series with the circuit)
- Resistors for current limiting
Parallel Combination
Setup: All resistors connected between the same two points (multiple paths).
Key property: Same voltage (V) across all resistors.
Derivation:
- Current through R₁: I₁ = V/R₁
- Current through R₂: I₂ = V/R₂
- Current through R₃: I₃ = V/R₃
- Total current: I = I₁ + I₂ + I₃ = V/R₁ + V/R₂ + V/R₃ = V(1/R₁ + 1/R₂ + 1/R₃)
- But I = V/R_equivalent
The equivalent resistance in parallel is less than the smallest individual resistance.
Applications of parallel circuits:
- Household wiring — every appliance gets the full supply voltage; failure of one does not affect others
- Car electrical systems
- When multiple paths for current are needed
Joule's Law
Statement: The amount of heat produced in a conductor is: 1. Directly proportional to the square of the current (I²) 2. Directly proportional to the resistance (R) 3. Directly proportional to the time (t) for which current flows
Mathematical form:
Where Q = heat produced (J), I = current (A), R = resistance (Ω), t = time (s)
Derivation
When a current I flows through a resistor R for time t:
The work done by the electric current (= electrical energy supplied) = charge × potential difference
- Charge flowing in time t: q = It
- Work done: W = qV = ItV
By Ohm's Law, V = IR:
- W = It × IR = I²Rt
If all this electrical energy is converted to heat (in a purely resistive circuit):
Alternative form (using V = IR):
Applications of Heating Effect of Electric Current
| Device | Principle |
|---|---|
| Electric iron | Nichrome wire gets hot due to I²Rt |
| Electric heater/room heater | Nichrome coil radiates heat |
| Incandescent bulb | Tungsten filament heated to incandescence (over 2500°C) |
| Electric fuse | Thin wire melts when excessive current flows — protects circuit |
| Electric kettle / water heater | Submerged heating element |
| Toaster | Nichrome coils |
Why nichrome wire is used:
- High resistivity → produces more heat for given current
- High melting point → withstands high temperatures
- Does not oxidise (corrode) at high temperatures
Domestic Electrical Wiring
In India, domestic supply is 220 V AC at 50 Hz (alternating current).
Three-wire system entering every house:
| Wire | Colour | Function |
|---|---|---|
| Live wire (L) | Red or brown | Carries current at 220 V |
| Neutral wire (N) | Black or blue | Return path at 0 V (earthed at substation) |
| Earth wire (E) | Green or yellow-green | Safety — connected to earth/ground |
Distribution inside the house:
1. Main switch / meter — electricity meter measures consumption (in kWh/units) 2. Main fuse board / MCB panel — distributes to different circuits (lighting, fans, power points) 3. Separate circuits:
4. All circuits are connected in parallel so each gets 220 V and failure of one doesn't affect others
- Lighting circuit: 5 A
- Power circuit (appliances): 15 A
Role of Fuse
Fuse is a safety device made of a thin wire of low melting point alloy (tin-lead alloy) connected in series with the circuit.
- If current exceeds the safe limit (due to short circuit or overload), the fuse wire heats up rapidly (Joule's Law: Q = I²Rt)
- The fuse wire melts (blows), breaking the circuit
- This prevents damage to appliances and fire
Types:
- Rewirable fuse: Old type; fuse wire replaced manually
- Cartridge fuse: Enclosed in a ceramic body
- MCB (Miniature Circuit Breaker): Modern equivalent; automatically trips and can be reset — no wire to replace
Fuse rating: Fuse must be rated slightly above the normal operating current of the circuit.
Role of Earthing
Earthing connects the metal body/casing of electrical appliances to the earth through the earth wire.
Purpose:
- If the live wire accidentally touches the metal casing of an appliance (due to insulation failure), the metal body becomes live at 220 V
- Without earthing, a person touching the appliance would get an electric shock (current flows through body to earth)
- With earthing, the fault current flows harmlessly through the low-resistance earth wire to ground
- The large fault current also blows the fuse, disconnecting the supply
Important: Earthing and fuse together provide two levels of protection — earthing provides a safe path; fuse disconnects the supply.
Electric Power
Definition: Electric power is the rate at which electrical energy is consumed (or work is done) in an electric circuit.
Unit: Watt (W) = 1 J/s; larger unit: kilowatt (kW) = 1000 W
Derivation:
- Work done in time t = charge × voltage = q × V
- Power P = W/t = (qV)/t = (q/t) × V = IV
- Substituting V = IR: P = I × IR = I²R
- Substituting I = V/R: P = V × V/R = V²/R
Electricity Billing
Unit of electrical energy = 1 kWh (kilowatt-hour)
1 kWh is the energy consumed by a 1 kW appliance running for 1 hour.
Cost of electricity:
Worked Problem:
A household uses the following appliances daily:
- 5 bulbs of 60 W each: 6 hours/day
- 1 fan of 75 W: 10 hours/day
- 1 TV of 120 W: 4 hours/day
- 1 refrigerator of 150 W: 24 hours/day
Calculate the monthly electricity bill if the rate is ₹5 per unit.
| Appliance | Power (W) | Hours/day | Units/day (kWh) |
|---|---|---|---|
| 5 bulbs | 5 × 60 = 300 W | 6 | 0.3 × 6 = 1.8 |
| Fan | 75 W | 10 | 0.075 × 10 = 0.75 |
| TV | 120 W | 4 | 0.12 × 4 = 0.48 |
| Refrigerator | 150 W | 24 | 0.15 × 24 = 3.6 |
Total units per day = 1.8 + 0.75 + 0.48 + 3.6 = 6.63 kWh/day
Units per month (30 days) = 6.63 × 30 = 198.9 ≈ 199 units
Monthly bill = 199 × ₹5 = ₹995
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