Very Short Questions: Electricity

Q1: How does the resistance of a wire change when:
(a) Its length is tripled?
(b) Its diameter is tripled?
(c) Its material is changed to one whose resistivity is three time?
Ans: (a) The resistance is tripled. This is because resistance R ∝ length (L), so if L becomes 3L, R becomes 3R.
(b) The resistance is reduced to one-ninth of its original value. Resistance R ∝ 1/area and area ∝ diameter², so tripling the diameter makes area 9 times larger and resistance 1/9 as before.
(c) The resistance is tripled. Resistance R ∝ resistivity (ρ), so if ρ becomes 3ρ, R becomes 3R.

Q2: If a wire is increased to 4 times its original length, by what factor does the resistivity change?
Ans: Resistivity does not change. Resistivity is a property of the material alone and is independent of the wire's length or shape, so it remains the same.

Q3: If the current passing through a conductor is doubled, what will be the change in the heat produced?
Ans: Heat produced will increase by four times. According to Joule's law, heat H ∝ I², so doubling I makes I² four times larger, hence H becomes 4H.

Q4: Name some devices which work on heating effect of electric current.
Ans:

• Electric bulb
• Electric iron
• Electric geyser
• Electric fuse

These devices convert electrical energy into heat; the heating effect is used for lighting, heating cloth, heating water, and protecting circuits respectively.

Q5: Why is an electric bulb filled with argon and nitrogen gas?
Ans: The bulb is filled with argon and a little nitrogen because these gases are inert (they do not react with hot tungsten). This prevents the tungsten filament from oxidising and reduces the rate of evaporation of the filament, thereby prolonging its life.

Q6: State the Joule's law of heating.
Ans: Joule's law of heating states that the heat produced in a resistor is directly proportional to:

• Square of current (I²)
• Resistance of the resistor (R)
• Time for which the current flows through the resistor (t).

Mathematically, H = I²Rt joules.

Using Ohm's law (V = IR), equivalent forms are H = VIt joules and H = V²t / R joules, where V is potential difference and t is time.

Q7: How is heating effect of electric current used in an electric bulb?
Ans: An electric bulb works on the heating effect of electric current. When current passes through a very thin, high-resistance tungsten filament, the filament heats up to a very high temperature (becomes white hot) and emits light. The emitted light is called incandescence.

Q8: Explain why, the filaments of electric bulbs are made of tungsten.
Ans: Tungsten is used because:

- It has a high resistivity, so it heats up well when current flows.

- It has a very high melting point (about 3,380 °C), so it can be kept white hot without melting.

- It is mechanically strong and has low vapour pressure at high temperature, which helps the filament last longer.

Q9: A current of 4 A flows through a 12V car headlight bulb for 10 minutes. How much energy transfer occurs during this time?
Ans: Given: I = 4 A, V = 12 V, t = 10 min = 10 × 60 = 600 s.

Energy transferred, E = V × I × t = 12 × 4 × 600 = 28,800 J.

Q10: An electric current of 4.0 A flows through a 12 Ω resistor. What is the rate at which heat energy is produced in the resistor?
Ans: Given: I = 4 A, R = 12 Ω.
Power (rate of heat production), P = I²R = (4.0)² × 12 = 16 × 12 = 192 W.

Q11: Calculate the energy transferred by a 5 A current flowing through a resistor of 2 Ω for 30 minutes.
Ans: Given: I = 5 A, R = 2 Ω, t = 30 min = 30 × 60 = 1,800 s.

Energy, E = I²Rt = (5)² × 2 × 1,800 = 25 × 2 × 1,800 = 90,000 J = 9 × 10⁴ J.

Q12: What does the slope of V - I graph at any point represent?
Ans: The slope represents resistance. Slope = ΔV/ΔI = R, so the steepness of the V-I line gives the resistance of the conductor.

Q13: What is the shape of the graph obtained by plotting potential difference applied across a conductor against the current flowing through it?

Ans: For an ohmic conductor the graph is a straight line (usually through the origin), showing V ∝ I according to Ohm's law.

Q14: Give reason why metals are good conductors, whereas non-metals are bad conductors of electricity.
Ans:

• Metals contain free (delocalised) electrons that can move easily and carry electric charge, so they conduct electricity well.
• Non-metals have electrons tightly bound to atoms and lack free charge carriers, so their resistivity is much higher and they conduct poorly.

Q15: Why are copper and aluminium wires usually employed for electricity transmission?

Ans: Copper and aluminium are used because they have low resistivity and so offer low energy loss as heat during transmission. Additionally, copper is highly conductive and mechanically strong, while aluminium is lighter and less expensive, making both suitable for transmission lines.