NEET Current Electricity — Set 20

Question 1

A $ 6 \, \Omega $ resistor carries a current of $ 3 \, \text{A} $ for $ 30 \, \text{s} $. What is the energy dissipated?

Accepted Answer

Energy: $ W = I^2 R t $. Substitute: $ W = 3^2 \times 6 \times 30 = 9 \times 180 = 1620 \, \text{J} $.

Question 2

A $ 21 \, \text{V} $ battery with negligible internal resistance is connected to a cubical network of 12 resistors, each $ 2.5 \, \Omega $. What is the total current?

Accepted Answer

Equivalent resistance: $ R_{\text{eq}} = \frac{5}{6} R = \frac{5}{6} \times 2.5 = \frac{12.5}{6} \approx 2.08 \, \Omega $. Total current: $ I = \frac{V}{R_{\text{eq}}} = \frac{21}{\frac{12.5}{6}} = 21 \times \frac{6}{12.5} = 10.08 \, \text{A} \approx 10.1 \, \text{A} $.

Question 3

A copper wire carries a current of $ 3 \, \text{A} $ with a drift speed of $ 1.2 \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}{8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times 1.2 \times 10^{-4}} $. Calculate: $ A = \frac{3}{1.632 \times 10^6} \approx 1.84 \times 10^{-6} \, \text{m}^2 $.

NEET Physics: Current Electricity — Practice Set 20

Q1. A \( 6 \, \Omega \) resistor carries a current of \( 3 \, \text{A} \) for \( 30 \, \text{s} \). What is the energy dissipated?

Q2. A \( 21 \, \text{V} \) battery with negligible internal resistance is connected to a cubical network of 12 resistors, each \( 2.5 \, \Omega \). What is the total current?

Q3. A copper wire carries a current of \( 3 \, \text{A} \) with a drift speed of \( 1.2 \times 10^{-4} \, \text{m/s} \). 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?

Q4. Two cells in parallel have emf \( 10 \, \text{V} \) and \( 4 \, \text{V} \) with internal resistances \( 5 \, \Omega \) and \( 2 \, \Omega \). What is the equivalent emf?

Q5. A \( 8 \, \Omega \) resistor dissipates \( 32 \, \text{W} \) of power. What is the current through it?

Q6. Why does the resistance of a conductor increase when its cross-sectional area is reduced?

Q7. Two cells in parallel have emf \( 15 \, \text{V} \) and \( 5 \, \text{V} \) with internal resistances \( 3 \, \Omega \) and \( 1 \, \Omega \). What is the equivalent internal resistance?

Q8. A \( 10 \, \Omega \) resistor dissipates \( 40 \, \text{W} \) of power. What is the voltage across it?

Q9. A Wheatstone bridge with \( R_1 = 7 \, \Omega \), \( R_2 = 14 \, \Omega \), \( R_3 = 21 \, \Omega \), \( R_4 = 42 \, \Omega \) has a \( 24 \, \text{V} \) battery across AC and a galvanometer (\( 4 \, \Omega \)) across BD. What is the current through the galvanometer?

Q10. A \( 5 \, \Omega \) resistor carries a current of \( 3 \, \text{A} \) for \( 20 \, \text{s} \). What is the energy dissipated?