NEET Current Electricity — Set 10

Question 1

A conductor has a resistivity of $ 6 \times 10^{-8} \, \Omega \text{m} $ and $ \alpha = 4 \times 10^{-3} \, ^\circ\text{C}^{-1} $ at $ 20^\circ \text{C} $. What is its resistivity at $ 90^\circ \text{C} $?

Accepted Answer

Use: $ \rho_t = \rho_0 [1 + \alpha (T - T_0)] $. Substitute: $ \rho_t = 6 \times 10^{-8} [1 + 4 \times 10^{-3} (90 - 20)] $. Calculate: $ \rho_t = 6 \times 10^{-8} [1 + 0.28] = 6 \times 10^{-8} \times 1.28 = 7.68 \times 10^{-8} \, \Omega \text{m} $.

Question 2

A copper wire carries $ 3.4 \, \text{A} $ with a drift speed of $ 1.25 \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?

Accepted Answer

Drift speed: $ v_d = \frac{I}{n e A} $. Rearrange: $ A = \frac{I}{n e v_d} $. Substitute: $ A = \frac{3.4}{8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times 1.25 \times 10^{-4}} $. Calculate: $ A = \frac{3.4}{1.7 \times 10^5} = 2.0 \times 10^{-5} \, \text{m}^2 $.

Question 3

A $ 5 \, \Omega $ resistor carries a current of $ 4 \, \text{A} $ for $ 15 \, \text{s} $. What is the energy dissipated?

Accepted Answer

Energy: $ W = I^2 R t $. Substitute: $ W = 4^2 \times 5 \times 15 = 16 \times 75 = 1200 \, \text{J} $.

NEET Physics: Current Electricity — Practice Set 10

Q1. A conductor has a resistivity of \( 6 \times 10^{-8} \, \Omega \text{m} \) and \( \alpha = 4 \times 10^{-3} \, ^\circ\text{C}^{-1} \) at \( 20^\circ \text{C} \). What is its resistivity at \( 90^\circ \text{C} \)?

Q2. A copper wire carries \( 3.4 \, \text{A} \) with a drift speed of \( 1.25 \times 10^{-4} \, \text{m/s} \). 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?

Q3. A \( 5 \, \Omega \) resistor carries a current of \( 4 \, \text{A} \) for \( 15 \, \text{s} \). What is the energy dissipated?

Q4. A Wheatstone bridge has \( R_1 = 30 \, \Omega \), \( R_2 = 60 \, \Omega \), \( R_3 = 25 \, \Omega \). What is \( R_4 \) for balance?

Q5. A circuit has a \( 6 \, \text{V} \) battery with \( 1 \, \Omega \) internal resistance and two resistors \( 2 \, \Omega \) and \( 3 \, \Omega \) in parallel. What is the total current?

Q6. A wire has a resistance of \( 25 \, \Omega \) at \( 20^\circ \text{C} \) and \( 27.5 \, \Omega \) at \( 90^\circ \text{C} \). What is the temperature coefficient of resistivity?

Q7. Two cells in parallel have emf \( 12 \, \text{V} \) and \( 6 \, \text{V} \) with internal resistances \( 4 \, \Omega \) and \( 2 \, \Omega \). What is the equivalent emf?

Q8. A circuit has a \( 30 \, \text{V} \) battery with \( 3 \, \Omega \) internal resistance and three resistors \( 3 \, \Omega \), \( 6 \, \Omega \), \( 12 \, \Omega \) in parallel. What is the current through the \( 6 \, \Omega \) resistor?

Q9. A \( 12 \, \text{V} \) battery with \( 1 \, \Omega \) internal resistance delivers a current of \( 2 \, \text{A} \) to a resistor. What is the resistance of the resistor?

Q10. What happens to the total resistance of a circuit when an additional resistor is added in parallel to an existing resistor?