NEET Current Electricity — Set 2

Question 1

A wire has a resistance of $ 15 \, \Omega $ at $ 20^\circ \text{C} $ and $ 16.5 \, \Omega $ at $ 70^\circ \text{C} $. What is the temperature coefficient of resistivity?

Accepted Answer

Use: $ R_t = R_0 [1 + \alpha (T - T_0)] $. Substitute: $ 16.5 = 15 [1 + \alpha (70 - 20)] $. Solve: $ 16.5 = 15 + 750\alpha \Rightarrow 750\alpha = 1.5 \Rightarrow \alpha = \frac{1.5}{750} = 2 \times 10^{-3} \, ^\circ\text{C}^{-1} $.

Question 2

A wire has a resistance of $ 30 \, \Omega $ at $ 25^\circ \text{C} $ and $ 31.5 \, \Omega $ at $ 75^\circ \text{C} $. What is the temperature coefficient of resistivity?

Accepted Answer

Use: $ R_t = R_0 [1 + \alpha (T - T_0)] $. Substitute: $ 31.5 = 30 [1 + \alpha (75 - 25)] $. Solve: $ 31.5 = 30 + 1500\alpha \Rightarrow 1500\alpha = 1.5 \Rightarrow \alpha = \frac{1.5}{1500} = 1.0 \times 10^{-3} \, ^\circ\text{C}^{-1} $.

Question 3

A nichrome wire has a resistance of $ 80 \, \Omega $ at $ 20^\circ \text{C} $ and $ \alpha = 1.7 \times 10^{-4} \, ^\circ\text{C}^{-1} $. What is its resistance at $ 300^\circ \text{C} $?

Accepted Answer

Use: $ R_t = R_0 [1 + \alpha (T - T_0)] $. Substitute: $ R_t = 80 [1 + 1.7 \times 10^{-4} (300 - 20)] $. Calculate: $ R_t = 80 [1 + 1.7 \times 10^{-4} \times 280] = 80 [1 + 0.0476] = 80 \times 1.0476 \approx 83.81 \, \Omega $.

NEET Physics: Current Electricity — Practice Set 2

Q1. A wire has a resistance of \( 15 \, \Omega \) at \( 20^\circ \text{C} \) and \( 16.5 \, \Omega \) at \( 70^\circ \text{C} \). What is the temperature coefficient of resistivity?

Q2. A wire has a resistance of \( 30 \, \Omega \) at \( 25^\circ \text{C} \) and \( 31.5 \, \Omega \) at \( 75^\circ \text{C} \). What is the temperature coefficient of resistivity?

Q3. A nichrome wire has a resistance of \( 80 \, \Omega \) at \( 20^\circ \text{C} \) and \( \alpha = 1.7 \times 10^{-4} \, ^\circ\text{C}^{-1} \). What is its resistance at \( 300^\circ \text{C} \)?

Q4. A copper wire of cross-sectional area \( 6 \times 10^{-7} \, \text{m}^2 \) carries a current of \( 1.8 \, \text{A} \). 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. In a Wheatstone bridge, if the bridge is unbalanced, what determines the direction of current through the galvanometer?

Q6. In a circuit with a battery, if the external resistance is reduced to zero, what limits the current?

Q7. A circuit has a \( 18 \, \text{V} \) battery with \( 3 \, \Omega \) internal resistance and three resistors \( 4 \, \Omega \), \( 8 \, \Omega \), \( 16 \, \Omega \) in parallel. What is the current through the \( 8 \, \Omega \) resistor?

Q8. A \( 10 \, \text{V} \) battery with negligible internal resistance is connected to a \( 2 \, \Omega \) and \( 3 \, \Omega \) resistor in series. What is the power dissipated in the \( 3 \, \Omega \) resistor?

Q9. A \( 45 \, \text{V} \) battery with negligible internal resistance is connected to a cubical network of 12 resistors, each \( 5 \, \Omega \). What is the total current?

Q10. In a metallic conductor, if the temperature increases significantly, what happens to the conductivity of the material?