NEET Current Electricity — Set 15

Question 1

A $ 15 \, \text{V} $ battery with $ 3 \, \Omega $ internal resistance delivers a current of $ 2 \, \text{A} $ to a resistor. What is the resistance of the resistor?

Accepted Answer

Terminal voltage: $ V = \varepsilon - I r = 15 - 2 \times 3 = 9 \, \text{V} $. Resistance: $ R = \frac{V}{I} = \frac{9}{2} = 4.5 \, \Omega $.

Question 2

A conductor has a resistivity of $ 1.0 \times 10^{-7} \, \Omega \text{m} $ and $ \alpha = 4 \times 10^{-3} \, ^\circ\text{C}^{-1} $ at $ 25^\circ \text{C} $. What is its resistivity at $ 85^\circ \text{C} $?

Accepted Answer

Use: $ \rho_t = \rho_0 [1 + \alpha (T - T_0)] $. Substitute: $ \rho_t = 1.0 \times 10^{-7} [1 + 4 \times 10^{-3} (85 - 25)] $. Calculate: $ \rho_t = 1.0 \times 10^{-7} [1 + 0.24] = 1.0 \times 10^{-7} \times 1.24 = 1.24 \times 10^{-7} \, \Omega \text{m} $.

Question 3

A platinum wire has a resistance of $ 6 \, \Omega $ at $ 0^\circ \text{C} $ and $ 6.48 \, \Omega $ at $ 100^\circ \text{C} $. What is the temperature coefficient of resistivity?

Accepted Answer

Use: $ R_t = R_0 [1 + \alpha (T - T_0)] $. Substitute: $ 6.48 = 6 [1 + \alpha (100 - 0)] $. Solve: $ 6.48 = 6 + 600\alpha \Rightarrow 600\alpha = 0.48 \Rightarrow \alpha = \frac{0.48}{600} = 8 \times 10^{-4} \, ^\circ\text{C}^{-1} $.

NEET Physics: Current Electricity — Practice Set 15

Q1. A \( 15 \, \text{V} \) battery with \( 3 \, \Omega \) internal resistance delivers a current of \( 2 \, \text{A} \) to a resistor. What is the resistance of the resistor?

Q2. A conductor has a resistivity of \( 1.0 \times 10^{-7} \, \Omega \text{m} \) and \( \alpha = 4 \times 10^{-3} \, ^\circ\text{C}^{-1} \) at \( 25^\circ \text{C} \). What is its resistivity at \( 85^\circ \text{C} \)?

Q3. A platinum wire has a resistance of \( 6 \, \Omega \) at \( 0^\circ \text{C} \) and \( 6.48 \, \Omega \) at \( 100^\circ \text{C} \). What is the temperature coefficient of resistivity?

Q4. A copper wire of cross-sectional area \( 3 \times 10^{-7} \, \text{m}^2 \) carries a current of \( 0.9 \, \text{A} \). If \( n = 8.5 \times 10^{28} \, \text{m}^{-3} \) and \( e = 1.6 \times 10^{-19} \, \text{C} \), what is the drift speed?

Q5. Two cells in parallel have emf \( 6 \, \text{V} \) and \( 4 \, \text{V} \) with internal resistances \( 2 \, \Omega \) and \( 1 \, \Omega \). What is the equivalent emf?

Q6. In a Wheatstone bridge with \( R_1 = 30 \, \Omega \), \( R_2 = 60 \, \Omega \), \( R_3 = 15 \, \Omega \), and \( R_4 = 32 \, \Omega \), a \( 10 \, \text{V} \) battery is connected across AC. What is the current through the galvanometer (\( R_g = 10 \, \Omega \))?

Q7. Two cells of emf \( 3 \, \text{V} \) and \( 5 \, \text{V} \) with internal resistances \( 1 \, \Omega \) and \( 3 \, \Omega \) are connected in series with a \( 4 \, \Omega \) resistor. What is the current through the circuit?

Q8. A nichrome wire has a resistance of \( 50 \, \Omega \) at \( 20^\circ \text{C} \) and \( \alpha = 1.7 \times 10^{-4} \, ^\circ\text{C}^{-1} \). What is its resistance at \( 380^\circ \text{C} \)?

Q9. A nichrome wire has a resistance of \( 80 \, \Omega \) at \( 25^\circ \text{C} \) and \( \alpha = 1.7 \times 10^{-4} \, ^\circ\text{C}^{-1} \). What is its resistance at \( 225^\circ \text{C} \)?

Q10. A battery of emf \( 12 \, \text{V} \) and internal resistance \( 1 \, \Omega \) is connected to a \( 5 \, \Omega \) resistor. What is the power dissipated in the external resistor?