NEET Current Electricity — Set 23

Question 1

A Wheatstone bridge has $ R_1 = 26 \, \Omega $, $ R_2 = 52 \, \Omega $, $ R_3 = 20 \, \Omega $. What is $ R_4 $ for balance?

Accepted Answer

Balance condition: $ \frac{R_1}{R_2} = \frac{R_3}{R_4} $. Substitute: $ \frac{26}{52} = \frac{20}{R_4} $. Solve: $ 0.5 = \frac{20}{R_4} \Rightarrow R_4 = \frac{20}{0.5} = 40 \, \Omega $.

Question 2

A copper wire carries $ 4.5 \, \text{A} $ with a drift speed of $ 1.8 \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{4.5}{8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times 1.8 \times 10^{-4}} $. Calculate: $ A = \frac{4.5}{2.448 \times 10^5} \approx 1.84 \times 10^{-5} \, \text{m}^2 $.

Question 3

A $ 12 \, \Omega $ resistor dissipates $ 48 \, \text{W} $ of power. What is the current through it?

Accepted Answer

Power: $ P = I^2 R $. Rearrange: $ I = \sqrt{\frac{P}{R}} $. Substitute: $ I = \sqrt{\frac{48}{12}} = \sqrt{4} = 2 \, \text{A} $.

NEET Physics: Current Electricity — Practice Set 23

Q1. A Wheatstone bridge has \( R_1 = 26 \, \Omega \), \( R_2 = 52 \, \Omega \), \( R_3 = 20 \, \Omega \). What is \( R_4 \) for balance?

Q2. A copper wire carries \( 4.5 \, \text{A} \) with a drift speed of \( 1.8 \times 10^{-4} \, \text{m/s} \). 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 \( 12 \, \Omega \) resistor dissipates \( 48 \, \text{W} \) of power. What is the current through it?

Q4. A conductor has a resistivity of \( 5 \times 10^{-8} \, \Omega \text{m} \) and \( \alpha = 4 \times 10^{-3} \, ^\circ\text{C}^{-1} \) at \( 30^\circ \text{C} \). What is its resistivity at \( 100^\circ \text{C} \)?

Q5. What is the primary reason a battery’s terminal voltage is less than its emf when supplying current?

Q6. Why does the current density in a conductor remain uniform across its cross-section under steady-state conditions?

Q7. A Wheatstone bridge has \( R_1 = 15 \, \Omega \), \( R_2 = 45 \, \Omega \), \( R_3 = 10 \, \Omega \). What is \( R_4 \) for balance?

Q8. In a circuit with two cells of different emfs connected in parallel, why is the equivalent emf not simply the sum of the individual emfs?

Q9. What happens to the current in a conductor if its cross-sectional area is doubled while keeping the potential difference and length constant?

Q10. A \( 12 \, \text{V} \) battery with negligible internal resistance is connected to a \( 4 \, \Omega \) and \( 8 \, \Omega \) resistor in series. What is the power dissipated in the \( 4 \, \Omega \) resistor?