Temperature Dependence of Resistance
Current Electricity
19
JEE Qs
8%
Hard
60
min
Always identify the material type (metal, semiconductor, alloy) to correctly determine the sign and magnitude of the temperature coefficient (α), and carefully align the reference resistance (R_0) with its corresponding temperature (T_0) in calculations.
🧮 Key Formulas
✅ Key Points for JEE
- 1For most metals, resistance increases linearly with temperature (positive temperature coefficient, α > 0) over a limited range due to increased electron-lattice scattering.
- 2For semiconductors and insulators, resistance generally decreases exponentially with increasing temperature (negative temperature coefficient, α < 0) due to increased charge carrier concentration.
- 3Alloys like Nichrome and Manganin have a very small temperature coefficient of resistance (α ≈ 0), making them suitable for standard resistors and heating elements where stable resistance is desired.
- 4The temperature coefficient of resistance (α) is defined as the fractional change in resistance per unit change in temperature, and it can be slightly temperature-dependent, though often assumed constant in JEE problems.
- 5Always ensure that the reference temperature (T_0) used for R_0 in the formula corresponds to the given initial resistance value; do not implicitly assume 0°C if not specified.
⚠️ Common Mistakes
- ✕Incorrectly using absolute temperatures instead of the temperature difference (ΔT) in the formula, or mixing units (e.g., Celsius for one temperature, Kelvin for another).
- ✕Assuming α is always positive; for semiconductors, it is negative, and this distinction is crucial.
- ✕Ignoring the specified reference temperature (T_0) for R_0 and wrongly using resistance at 0°C for R_0 when it's defined at a different reference temperature.
- ✕Applying the simple linear approximation R_T = R_0(1 + αΔT) to semiconductors without considering the more accurate exponential dependence for larger temperature ranges.
📝 Practice Questions
See allQ47.The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be ____ A.
Q27.Given below are two statements : Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs. Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries. In the light of the above statements, choose the correct answer from the options given below. (1) Both Statement-I and Statement-II are false (2) Statement-I is false but Statement-II is true (3) Both Statement-I and Statement-II are true (4) Statement-I is true but Statement-II is false
Q34. Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance Rp = 1Ω as shown in the figure. An external resistance of Re = 2Ω is connected via the sliding contact. The electric current in the circuit is : (1) 0.9 A (2) 1.35 A (3) 0.3 A (4) 1.0 A 2025 (22 Jan Shift 1) JEE Main Previous Year Paper
Q45.Which of the following resistivity ( ρ ) v/s temperature (T) curves is most suitable to be used in wire bound standard resistors? (1) (2) (3) (4)
Q47.The net current flowing in the given circuit is_______ A.
Q30.Refer to the circuit diagram given in the figure. which of the following observations are correct? A. Total resistance of circuit is 6Ω B. Current in Ammeter is 1 A C. Potential across AB is 4 Volts. D. Potential across 2025 (23 Jan Shift 1) JEE Main Previous Year Paper CD is 4 Volts E. Total resistance of the circuit is 8Ω. Choose the correct answer from the options given below: (1) A, B and D Only (2) A, B and C Only (3) A, C and D Only (4) B, C and E Only
NCERT Chapters
- Class 12 Physics Ch 3: Current Electricity