✓ Board-verified
Physics · 2025 · 3 marks
CBSE 2025 · Region 2 · Set 3 · Q22
(a) Define Electrical conductivity. Obtain the expression of electrical conductivity of a conductor in terms of number density and relaxation time of…
(a)
Define Electrical conductivity. Obtain the expression of electrical conductivity of a conductor in terms of number density and relaxation time of free electrons.
(b)
Explain qualitative change in resistivity of a conductor with temperature using expression obtained in (a) .
Marking-scheme solution
(a)
Electrical conductivity: It is the reciprocal of the resistivity.
$\displaystyle \sigma=1 / \rho$
$\displaystyle I t=n e A v_{d} t$
Substituting $\displaystyle v_{d}=\frac{e E}{m} \tau$:
$\displaystyle I t=\frac{e^{2} A}{m} \tau n t E$
$\displaystyle I=j A$
$\displaystyle \Rightarrow j=\frac{n e^{2}}{m} \tau E$ .........($\displaystyle 1$)
$\displaystyle j=\sigma E$ .......................($\displaystyle 2$)
Comparing eq. ($\displaystyle 1$) & ($\displaystyle 2$):
$\displaystyle \sigma=\frac{n e^{2}}{m} \tau$
(b)
On increasing the temperature, the value of $\displaystyle \tau$ decreases, as a consequence conductivity decreases and hence resistivity increases.
All Current Electricity questions2025 question paperNCERT solutions: Current ElectricityPractice Current Electricity →
More from Current Electricity
- A steady current flows through a metallic wire whose area of cross-section increases continuously from one end of the wire to the other. The…2023
- (i) Define mobility of electrons. Give its SI units. (ii) A steady current flows through a wire AB, as shown in the figure. What happens to the…2023
- What is the order of magnitude of drift velocity of electrons in a conductor? Deduce the relation between the current flowing through a conductor and…2026
- 'Current is a scalar quantity, although we represent current with an arrow.' Explain. Derive the balance condition of a Wheatstone Bridge.2026
- The number of electrons flowing through a conductor per second is 3 · 3 × 10^19. The current flowing through the conductor is:2023
- A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the…2026
- Define current density and relaxation time. Derive an expression for resistivity of a conductor in terms of number density of charge carriers in the…2023
- A battery of e. m. f. 12 V and internal resistance 0.5 Ω is connected to a 9.5 Ω resistor through a key. The ratio of potential difference between…2025
CBSE Class 12 Physics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.