NEET Current Electricity — Set 24

Question 1

A $ 15 \, \text{V} $ battery with $ 1 \, \Omega $ internal resistance delivers a current of $ 2.5 \, \text{A} $ to a resistor. What is the resistance of the resistor?

Accepted Answer

Terminal voltage: $ V = \varepsilon - I r = 15 - 2.5 \times 1 = 12.5 \, \text{V} $. Resistance: $ R = \frac{V}{I} = \frac{12.5}{2.5} = 5 \, \Omega $.

Question 2

A copper wire carries $ 2.72 \, \text{A} $ with a drift speed of $ 8 \times 10^{-5} \, \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{2.72}{8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times 8 \times 10^{-5}} $. Calculate: $ A = \frac{2.72}{1.088 \times 10^5} \approx 2.5 \times 10^{-5} \, \text{m}^2 $.

Question 3

Why does the power dissipated in a resistor increase quadratically with current?

Accepted Answer

Power $ P = I^2 R $. Since power depends on the square of the current ($ I^2 $), doubling the current quadruples the power, assuming resistance remains constant.

NEET Physics: Current Electricity — Practice Set 24

Q1. A \( 15 \, \text{V} \) battery with \( 1 \, \Omega \) internal resistance delivers a current of \( 2.5 \, \text{A} \) to a resistor. What is the resistance of the resistor?

Q2. A copper wire carries \( 2.72 \, \text{A} \) with a drift speed of \( 8 \times 10^{-5} \, \text{m/s} \). 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. Why does the power dissipated in a resistor increase quadratically with current?

Q4. A wire of length \( 6 \, \text{m} \) and cross-sectional area \( 5 \times 10^{-6} \, \text{m}^2 \) has a resistance of \( 12 \, \Omega \). What is the resistivity of the material?

Q5. In a circuit with a battery, why does the internal resistance of the battery affect the maximum power delivered to an external load?

Q6. A copper wire carries \( 2 \, \text{A} \) with a drift speed of \( 8 \times 10^{-5} \, \text{m/s} \). 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?

Q7. What is the physical significance of the temperature coefficient of resistivity being positive for metals?

Q8. A conductor has a resistivity of \( 8 \times 10^{-8} \, \Omega \text{m} \) and \( \alpha = 4 \times 10^{-3} \, ^\circ\text{C}^{-1} \) at \( 20^\circ \text{C} \). What is its resistivity at \( 70^\circ \text{C} \)?

Q9. A Wheatstone bridge has \( R_1 = 18 \, \Omega \), \( R_2 = 36 \, \Omega \), \( R_3 = 12 \, \Omega \). What is \( R_4 \) for balance?

Q10. A circuit has a \( 10 \, \text{V} \) battery with \( 1 \, \Omega \) internal resistance and two resistors \( 5 \, \Omega \) and \( 10 \, \Omega \) in parallel. What is the total current?