NEET Current Electricity — Set 22

Question 1

A copper wire of cross-sectional area $ 5 \times 10^{-7} \, \text{m}^2 $ carries a current of $ 1 \, \text{A} $. If $ n = 8.5 \times 10^{28} \, \text{m}^{-3} $ and $ e = 1.6 \times 10^{-19} \, \text{C} $, what is the drift speed?

Accepted Answer

Drift speed: $ v_d = \frac{I}{n e A} $. Substitute: $ v_d = \frac{1}{8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times 5 \times 10^{-7}} $. Calculate: $ v_d = \frac{1}{6.8 \times 10^3} \approx 1.47 \times 10^{-4} \, \text{m/s} $.

Question 2

A wire of length $ 9 \, \text{m} $ and cross-sectional area $ 1.5 \times 10^{-6} \, \text{m}^2 $ has a resistance of $ 18 \, \Omega $. What is the resistivity of the material?

Accepted Answer

Resistance: $ R = \frac{\rho l}{A} $. Rearrange: $ \rho = \frac{R A}{l} $. Substitute: $ \rho = \frac{18 \times 1.5 \times 10^{-6}}{9} = 3 \times 10^{-6} \, \Omega \text{m} $.

Question 3

What happens to the drift velocity of electrons in a conductor if the conductor’s temperature increases while the applied electric field remains constant?

Accepted Answer

Drift velocity $ v_d = e E \tau / m $. As temperature increases, $ \tau $ (relaxation time) decreases due to more collisions, reducing $ v_d $ if $ E $ is constant.

NEET Physics: Current Electricity — Practice Set 22

Q1. A copper wire of cross-sectional area \( 5 \times 10^{-7} \, \text{m}^2 \) carries a current of \( 1 \, \text{A} \). If \( n = 8.5 \times 10^{28} \, \text{m}^{-3} \) and \( e = 1.6 \times 10^{-19} \, \text{C} \), what is the drift speed?

Q2. A wire of length \( 9 \, \text{m} \) and cross-sectional area \( 1.5 \times 10^{-6} \, \text{m}^2 \) has a resistance of \( 18 \, \Omega \). What is the resistivity of the material?

Q3. What happens to the drift velocity of electrons in a conductor if the conductor’s temperature increases while the applied electric field remains constant?

Q4. A wire has a resistance of \( 18 \, \Omega \) at \( 20^\circ \text{C} \) and \( 19.8 \, \Omega \) at \( 80^\circ \text{C} \). What is the temperature coefficient of resistivity?

Q5. A wire has a resistance of \( 10 \, \Omega \) at \( 20^\circ \text{C} \) and \( 12 \, \Omega \) at \( 100^\circ \text{C} \). What is the temperature coefficient of resistivity?

Q6. A cell of emf \( 9 \, \text{V} \) and internal resistance \( 1 \, \Omega \) is connected to a \( 8 \, \Omega \) resistor. What is the terminal voltage?

Q7. Why does a filament lamp deviate from Ohm’s law as current increases?

Q8. A \( 3 \, \text{m} \) long wire with a cross-sectional area of \( 1.5 \times 10^{-6} \, \text{m}^2 \) has a resistance of \( 6 \, \Omega \). What is the current density when a potential difference of \( 12 \, \text{V} \) is applied?

Q9. A Wheatstone bridge has \( R_1 = 25 \, \Omega \), \( R_2 = 50 \, \Omega \), \( R_3 = 20 \, \Omega \). What is \( R_4 \) for balance?

Q10. A wire of length \( 8 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) has a resistance of \( 16 \, \Omega \). What is the resistivity of the material?