NEET Current Electricity — Set 11

Question 1

A circuit has a $ 12 \, \text{V} $ battery with $ 2 \, \Omega $ internal resistance and three resistors $ 3 \, \Omega $, $ 6 \, \Omega $, $ 9 \, \Omega $ in parallel. What is the current through the $ 9 \, \Omega $ resistor?

Accepted Answer

Parallel resistance: $ \frac{1}{R_p} = \frac{1}{3} + \frac{1}{6} + \frac{1}{9} = \frac{6 + 3 + 2}{18} = \frac{11}{18} \Rightarrow R_p = \frac{18}{11} \approx 1.64 \, \Omega $. Total resistance: $ R_{\text{total}} = 2 + 1.64 = 3.64 \, \Omega $. Total current: $ I = \frac{\varepsilon}{R_{\text{total}}} = \frac{12}{3.64} \approx 3.3 \, \text{A} $. Voltage across parallel: $ V = I R_p = 3.3 \times 1.64 \approx 5.41 \, \text{V} $. Current through $ 9 \, \Omega $: $ I_9 = \frac{V}{9} = \frac{5.41}{9} \approx 0.6 \, \text{A} $.

Question 2

A $ 6 \, \Omega $ resistor carries a current of $ 4 \, \text{A} $ for $ 5 \, \text{s} $. What is the energy dissipated?

Accepted Answer

Energy: $ W = I^2 R t $. Substitute: $ W = 4^2 \times 6 \times 5 = 16 \times 30 = 480 \, \text{J} $.

Question 3

A copper wire of cross-sectional area $ 4 \times 10^{-7} \, \text{m}^2 $ carries a current of $ 1.2 \, \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{1.2}{8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times 4 \times 10^{-7}} $. Calculate: $ v_d = \frac{1.2}{5.44 \times 10^3} \approx 2.21 \times 10^{-4} \, \text{m/s} $.

NEET Physics: Current Electricity — Practice Set 11

Q1. A circuit has a \( 12 \, \text{V} \) battery with \( 2 \, \Omega \) internal resistance and three resistors \( 3 \, \Omega \), \( 6 \, \Omega \), \( 9 \, \Omega \) in parallel. What is the current through the \( 9 \, \Omega \) resistor?

Q2. A \( 6 \, \Omega \) resistor carries a current of \( 4 \, \text{A} \) for \( 5 \, \text{s} \). What is the energy dissipated?

Q3. A copper wire of cross-sectional area \( 4 \times 10^{-7} \, \text{m}^2 \) carries a current of \( 1.2 \, \text{A} \). If \( n = 8.5 \times 10^{28} \, \text{m}^{-3} \) and \( e = 1.6 \times 10^{-19} \, \text{C} \), what is the drift speed?

Q4. A circuit has a \( 24 \, \text{V} \) battery with \( 3 \, \Omega \) internal resistance and three resistors \( 6 \, \Omega \), \( 12 \, \Omega \), \( 24 \, \Omega \) in parallel. What is the current through the \( 12 \, \Omega \) resistor?

Q5. Why is high voltage used in power transmission lines to reduce energy loss?

Q6. Why does the emf of a cell depend on its chemical composition rather than its size?

Q7. A cell of emf \( 4 \, \text{V} \) and internal resistance \( 0.5 \, \Omega \) is connected to a \( 3.5 \, \Omega \) resistor. What is the current in the circuit?

Q8. A copper wire of cross-sectional area \( 4 \times 10^{-7} \, \text{m}^2 \) carries a current of \( 1.36 \, \text{A} \). If \( n = 8.5 \times 10^{28} \, \text{m}^{-3} \) and \( e = 1.6 \times 10^{-19} \, \text{C} \), what is the drift speed?

Q9. What happens to the current density in a conductor if the conductor is stretched to twice its original length without changing the applied voltage?

Q10. A Wheatstone bridge with \( R_1 = 6 \, \Omega \), \( R_2 = 12 \, \Omega \), \( R_3 = 9 \, \Omega \), \( R_4 = 18 \, \Omega \) has a \( 15 \, \text{V} \) battery across AC and a galvanometer (\( 5 \, \Omega \)) across BD. What is the current through the galvanometer?