NEET Current Electricity — Set 8

Question 1

When two identical resistors are connected in series and then in parallel, how does the equivalent resistance change?

Accepted Answer

For resistors $ R $ in series: $ R_{\text{eq}} = R + R = 2R $. In parallel: $ 1/R_{\text{eq}} = 1/R + 1/R = 2/R \Rightarrow R_{\text{eq}} = R/2 $. The series resistance (2R) is four times the parallel resistance (R/2), as $ 2R / (R/2) = 4 $.

Question 2

A Wheatstone bridge has $ R_1 = 16 \, \Omega $, $ R_2 = 32 \, \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{16}{32} = \frac{20}{R_4} $. Solve: $ 0.5 = \frac{20}{R_4} \Rightarrow R_4 = \frac{20}{0.5} = 40 \, \Omega $.

Question 3

A wire of length $ 12 \, \text{m} $ and cross-sectional area $ 3 \times 10^{-6} \, \text{m}^2 $ has a resistance of $ 24 \, \Omega $. What is the resistivity of the material?

Accepted Answer

Resistance: $ R = \frac{\rho l}{A} $. Rearrange: $ \rho = \frac{R A}{l} $. Substitute: $ \rho = \frac{24 \times 3 \times 10^{-6}}{12} = 6 \times 10^{-6} \, \Omega \text{m} $.

NEET Physics: Current Electricity — Practice Set 8

Q1. When two identical resistors are connected in series and then in parallel, how does the equivalent resistance change?

Q2. A Wheatstone bridge has \( R_1 = 16 \, \Omega \), \( R_2 = 32 \, \Omega \), \( R_3 = 20 \, \Omega \). What is \( R_4 \) for balance?

Q3. A wire of length \( 12 \, \text{m} \) and cross-sectional area \( 3 \times 10^{-6} \, \text{m}^2 \) has a resistance of \( 24 \, \Omega \). What is the resistivity of the material?

Q4. Two cells in parallel have emf \( 6 \, \text{V} \) and \( 3 \, \text{V} \) with internal resistances \( 3 \, \Omega \) and \( 1 \, \Omega \). What is the equivalent emf?

Q5. In a circuit with two resistors in series, why does the voltage divide proportionally to their resistances?

Q6. A wire of length \( 3 \, \text{m} \) and resistance \( 6 \, \Omega \) is stretched to \( 6 \, \text{m} \). What is the new resistance?

Q7. A copper wire of cross-sectional area \( 1 \times 10^{-6} \, \text{m}^2 \) carries a current of \( 1.5 \, \text{A} \). If \( n = 8.5 \times 10^{28} \, \text{m}^{-3} \) and \( e = 1.6 \times 10^{-19} \, \text{C} \), what is the drift speed?

Q8. Why does the drift velocity of electrons in a conductor remain constant despite continuous acceleration by an electric field?

Q9. A circuit has a \( 15 \, \text{V} \) battery with \( 2 \, \Omega \) internal resistance and three resistors \( 3 \, \Omega \), \( 6 \, \Omega \), \( 12 \, \Omega \) in parallel. What is the current through the \( 6 \, \Omega \) resistor?

Q10. A Wheatstone bridge with \( R_1 = 5 \, \Omega \), \( R_2 = 10 \, \Omega \), \( R_3 = 15 \, \Omega \), \( R_4 = 30 \, \Omega \) has a \( 18 \, \text{V} \) battery across AC and a galvanometer (\( 3 \, \Omega \)) across BD. What is the current through the galvanometer?