Temperature Dependence of Resistance - UNSOLVED PRACTICE SET
Chapter: Current Electricity | Topic: Temperature Dependence of Resistance
TEMPERATURE DEPENDENCE OF RESISTANCE - UNSOLVED PRACTICE SET
Topic: Temperature Dependence of Resistance
Multiple Choice Questions
Q1. The resistance of a metallic conductor increases with temperature because:
- The number of free electrons increases
- The relaxation time of electrons decreases
- The length of the conductor decreases
- The cross-sectional area increases
Q2. The temperature coefficient of resistance α is defined as:
- The change in resistance per unit resistance per unit temperature change
- The change in resistance per unit temperature change
- The resistance at 0°C
- The rate of change of temperature with resistance
Q3. For metals, the temperature coefficient of resistance is:
- Negative
- Positive
- Zero
- Infinite
Q4. For semiconductors, the temperature coefficient of resistance is:
- Positive
- Negative
- Zero
- Very large and positive
Q5. The resistance of a conductor at temperature T is given by:
- R = R₀(1 − αT)
- R = R₀(1 + αT)
- R = R₀/(1 + αT)
- R = R₀αT
Q6. A carbon resistor has resistance 100 Ω at 20°C. If its temperature coefficient is −0.0005 /°C, its resistance at 120°C will be:
- 105 Ω
- 95 Ω
- 100 Ω
- 150 Ω
Short Answer Questions
Q7. Define temperature coefficient of resistance. What is its SI unit?
Q8. Why does the resistance of a metal increase with temperature while that of a semiconductor decreases?
Q9. A copper wire has resistance 10 Ω at 20°C. Its temperature coefficient is 4 × 10⁻³ /°C. Calculate its resistance at 80°C.
Q10. Why is nichrome used in heating elements rather than copper, even though copper is a better conductor?
Q11. Explain why the filament of an electric bulb has much higher resistance when glowing than when cold.
Q12. A platinum wire has resistance 4 Ω at 0°C and 4.5 Ω at 100°C. Calculate its temperature coefficient of resistance.
Long Answer Questions
Q13. Explain the temperature dependence of resistance for metals and semiconductors at the atomic level. Why do they show opposite behavior? Use the concept of relaxation time and charge carriers.
Q14. A metal wire has resistance R₁ at temperature T₁ and R₂ at temperature T₂. Derive the expression for the temperature coefficient of resistance α. Explain the assumptions made in this derivation.
Q15. An electric bulb rated 100 W, 220 V has a tungsten filament. The resistance of the filament at room temperature (20°C) is measured to be 40 Ω.
(a) Calculate the resistance of the filament when the bulb is operating at its rated power.
(b) Estimate the operating temperature of the filament. [Given: α for tungsten = 4.5 × 10⁻³ /°C]
(c) Why is the initial current when the bulb is switched on much higher than the steady current?
(d) Explain why this "inrush current" can sometimes cause bulbs to blow when switched on.
Numerical / Application-Based Problems
Q16. In a school physics lab, a student performs an experiment to study the temperature dependence of resistance using a nichrome wire.
(a) The wire has resistance 20 Ω at 20°C. The temperature coefficient of nichrome is 1.7 × 10⁻⁴ /°C. Calculate its resistance at 200°C.
(b) If a current of 2 A flows through the wire at 200°C, calculate the power dissipated and the rate of temperature rise (assume no heat loss). [Given: mass of wire = 5 g, specific heat capacity = 450 J/kg°C]
(c) How long will it take for the wire to reach 300°C from 200°C under these conditions?
(d) Explain why in practice, the wire temperature would not rise indefinitely.
Q17. A platinum resistance thermometer has resistance 10 Ω at 0°C and 14 Ω at 100°C. It is used to measure the temperature of an oven.
(a) Calculate the temperature coefficient of resistance for platinum.
(b) If the resistance of the thermometer in the oven is 16 Ω, what is the oven temperature?
(c) At what temperature will the resistance be 20 Ω?
(d) Why is platinum preferred over other metals for resistance thermometers?
Q18. Two wires A and B of the same length and diameter are connected in series. Wire A is made of copper (α = 4 × 10⁻³ /°C) and wire B is made of nichrome (α = 1.7 × 10⁻⁴ /°C). At 20°C, both have the same resistance R.
(a) Calculate the ratio of their resistances at 120°C.
(b) If the combination is connected to a constant voltage source, how does the current change as temperature increases from 20°C to 120°C?
(c) Calculate the effective temperature coefficient of the series combination.
(d) Explain why the series combination has a temperature coefficient closer to that of copper than nichrome.