NEET Current Electricity — Set 6

Question 1

A nichrome wire has a resistance of $ 70 \, \Omega $ at $ 30^\circ \text{C} $ and $ \alpha = 1.7 \times 10^{-4} \, ^\circ\text{C}^{-1} $. What is its resistance at $ 270^\circ \text{C} $?

Accepted Answer

Use: $ R_t = R_0 [1 + \alpha (T - T_0)] $. Substitute: $ R_t = 70 [1 + 1.7 \times 10^{-4} (270 - 30)] $. Calculate: $ R_t = 70 [1 + 1.7 \times 10^{-4} \times 240] = 70 [1 + 0.0408] = 70 \times 1.0408 = 72.86 \, \Omega $.

Question 2

A wire of length $ 5 \, \text{m} $ and resistance $ 10 \, \Omega $ is stretched to $ 10 \, \text{m} $. What is the new resistance?

Accepted Answer

Volume constant: $ l A = l' A' \Rightarrow A' = \frac{A}{2} $. New resistance: $ R' = \frac{\rho l'}{A'} = \frac{\rho (2l)}{\frac{A}{2}} = 4 \frac{\rho l}{A} = 4R = 4 \times 10 = 40 \, \Omega $.

Question 3

A nichrome wire has a resistance of $ 90 \, \Omega $ at $ 20^\circ \text{C} $ and $ \alpha = 1.7 \times 10^{-4} \, ^\circ\text{C}^{-1} $. What is its resistance at $ 260^\circ \text{C} $?

Accepted Answer

Use: $ R_t = R_0 [1 + \alpha (T - T_0)] $. Substitute: $ R_t = 90 [1 + 1.7 \times 10^{-4} (260 - 20)] $. Calculate: $ R_t = 90 [1 + 1.7 \times 10^{-4} \times 240] = 90 [1 + 0.0408] = 90 \times 1.0408 = 93.67 \, \Omega $.

NEET Physics: Current Electricity — Practice Set 6

Q1. A nichrome wire has a resistance of \( 70 \, \Omega \) at \( 30^\circ \text{C} \) and \( \alpha = 1.7 \times 10^{-4} \, ^\circ\text{C}^{-1} \). What is its resistance at \( 270^\circ \text{C} \)?

Q2. A wire of length \( 5 \, \text{m} \) and resistance \( 10 \, \Omega \) is stretched to \( 10 \, \text{m} \). What is the new resistance?

Q3. A nichrome wire has a resistance of \( 90 \, \Omega \) at \( 20^\circ \text{C} \) and \( \alpha = 1.7 \times 10^{-4} \, ^\circ\text{C}^{-1} \). What is its resistance at \( 260^\circ \text{C} \)?

Q4. A Wheatstone bridge with \( R_1 = 12 \, \Omega \), \( R_2 = 24 \, \Omega \), \( R_3 = 18 \, \Omega \), \( R_4 = 36 \, \Omega \) has a \( 12 \, \text{V} \) battery across AC and a galvanometer (\( 5 \, \Omega \)) across BD. What is the current through the galvanometer?

Q5. Why does a battery’s emf remain constant even when it delivers a large current?

Q6. A \( 14 \, \text{V} \) battery with \( 2 \, \Omega \) internal resistance delivers a current of \( 2 \, \text{A} \) to a resistor. What is the resistance of the resistor?

Q7. Why does a conductor’s current density increase when its length is halved while keeping the potential difference constant?

Q8. A conductor has a resistivity of \( 9 \times 10^{-8} \, \Omega \text{m} \) and \( \alpha = 4 \times 10^{-3} \, ^\circ\text{C}^{-1} \) at \( 20^\circ \text{C} \). What is its resistivity at \( 60^\circ \text{C} \)?

Q9. Two cells of emf \( 4 \, \text{V} \) and \( 5 \, \text{V} \) with internal resistances \( 0.5 \, \Omega \) and \( 1 \, \Omega \) are connected in series with a \( 5.5 \, \Omega \) resistor. What is the current through the circuit?

Q10. A \( 15 \, \text{V} \) battery with negligible internal resistance is connected to a \( 3 \, \Omega \) and \( 9 \, \Omega \) resistor in series. What is the power dissipated in the \( 9 \, \Omega \) resistor?