NEET Current Electricity — Set 21

Question 1

A $ 12 \, \text{V} $ battery with $ 2 \, \Omega $ internal resistance delivers a current of $ 3 \, \text{A} $ to a resistor. What is the resistance of the resistor?

Accepted Answer

Terminal voltage: $ V = \varepsilon - I r = 12 - 3 \times 2 = 6 \, \text{V} $. Resistance: $ R = \frac{V}{I} = \frac{6}{3} = 2 \, \Omega $.

Question 2

Why does a superconductor exhibit zero resistance below its critical temperature?

Accepted Answer

Below the critical temperature, electrons in a superconductor form Cooper pairs, which move without scattering off lattice ions, eliminating resistance as there’s no energy loss to collisions.

Question 3

A nichrome wire has a resistance of $ 50 \, \Omega $ at $ 25^\circ \text{C} $ and $ 55 \, \Omega $ at a higher temperature. If $ \alpha = 1.7 \times 10^{-4} \, ^\circ\text{C}^{-1} $, what is the temperature?

Accepted Answer

Use: $ R_t = R_0 [1 + \alpha (T - T_0)] $. Substitute: $ 55 = 50 [1 + 1.7 \times 10^{-4} (T - 25)] $. Solve: $ 55 = 50 + 50 \times 1.7 \times 10^{-4} (T - 25) \Rightarrow 5 = 8.5 \times 10^{-3} (T - 25) $. $ T - 25 = \frac{5}{8.5 \times 10^{-3}} \approx 588 \Rightarrow T \approx 613^\circ \text{C} $.

NEET Physics: Current Electricity — Practice Set 21

Q1. A \( 12 \, \text{V} \) battery with \( 2 \, \Omega \) internal resistance delivers a current of \( 3 \, \text{A} \) to a resistor. What is the resistance of the resistor?

Q2. Why does a superconductor exhibit zero resistance below its critical temperature?

Q3. A nichrome wire has a resistance of \( 50 \, \Omega \) at \( 25^\circ \text{C} \) and \( 55 \, \Omega \) at a higher temperature. If \( \alpha = 1.7 \times 10^{-4} \, ^\circ\text{C}^{-1} \), what is the temperature?

Q4. Why does the equivalent resistance of two resistors in parallel always lie between zero and the smallest individual resistance?

Q5. A \( 5 \, \Omega \) resistor carries a current of \( 3 \, \text{A} \) for \( 20 \, \text{s} \). What is the energy dissipated?

Q7. A \( 7 \, \Omega \) resistor carries a current of \( 2 \, \text{A} \) for \( 25 \, \text{s} \). What is the energy dissipated?

Q8. Why does the resistivity of an insulator decrease dramatically when impurities are added?

Q9. A copper wire carries \( 4 \, \text{A} \) with a drift speed of \( 1.0 \times 10^{-4} \, \text{m/s} \). If \( n = 8.5 \times 10^{28} \, \text{m}^{-3} \) and \( e = 1.6 \times 10^{-19} \, \text{C} \), what is the cross-sectional area?

Q10. A conductor of length \( 1 \, \text{m} \) and cross-sectional area \( 1 \times 10^{-6} \, \text{m}^2 \) has a resistance of \( 2 \, \Omega \). What is the resistivity of the material?