NEET Current Electricity — Set 7

Question 1

A $ 10 \, \text{V} $ battery with negligible internal resistance is connected to a cubical network of 12 resistors, each $ 1.5 \, \Omega $. What is the current through one edge from a corner?

Accepted Answer

Equivalent resistance: $ R_{\text{eq}} = \frac{5}{6} R = \frac{5}{6} \times 1.5 = 1.25 \, \Omega $. Total current: $ I_{\text{total}} = \frac{V}{R_{\text{eq}}} = \frac{10}{1.25} = 8 \, \text{A} $. Corner current: $ I = \frac{I_{\text{total}}}{3} = \frac{8}{3} \approx 2.67 \, \text{A} $.

Question 2

A copper wire of cross-sectional area $ 8 \times 10^{-7} \, \text{m}^2 $ carries a current of $ 2 \, \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?

Accepted Answer

Drift speed: $ v_d = \frac{I}{n e A} $. Substitute: $ v_d = \frac{2}{8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times 8 \times 10^{-7}} $. Calculate: $ v_d = \frac{2}{1.088 \times 10^4} \approx 1.84 \times 10^{-4} \, \text{m/s} $.

Question 3

A conductor has a resistivity of $ 1.2 \times 10^{-7} \, \Omega \text{m} $ and $ \alpha = 4 \times 10^{-3} \, ^\circ\text{C}^{-1} $ at $ 20^\circ \text{C} $. What is its resistivity at $ 80^\circ \text{C} $?

Accepted Answer

Use: $ \rho_t = \rho_0 [1 + \alpha (T - T_0)] $. Substitute: $ \rho_t = 1.2 \times 10^{-7} [1 + 4 \times 10^{-3} (80 - 20)] $. Calculate: $ \rho_t = 1.2 \times 10^{-7} [1 + 0.24] = 1.2 \times 10^{-7} \times 1.24 = 1.488 \times 10^{-7} \, \Omega \text{m} $.

NEET Physics: Current Electricity — Practice Set 7

Q1. A \( 10 \, \text{V} \) battery with negligible internal resistance is connected to a cubical network of 12 resistors, each \( 1.5 \, \Omega \). What is the current through one edge from a corner?

Q2. A copper wire of cross-sectional area \( 8 \times 10^{-7} \, \text{m}^2 \) carries a current of \( 2 \, \text{A} \). If \( n = 8.5 \times 10^{28} \, \text{m}^{-3} \) and \( e = 1.6 \times 10^{-19} \, \text{C} \), what is the drift speed?

Q3. A conductor has a resistivity of \( 1.2 \times 10^{-7} \, \Omega \text{m} \) and \( \alpha = 4 \times 10^{-3} \, ^\circ\text{C}^{-1} \) at \( 20^\circ \text{C} \). What is its resistivity at \( 80^\circ \text{C} \)?

Q4. A cell of emf \( 10 \, \text{V} \) and internal resistance \( 1 \, \Omega \) is connected to a \( 9 \, \Omega \) resistor. What is the terminal voltage?

Q5. Two cells in parallel have emf \( 12 \, \text{V} \) and \( 3 \, \text{V} \) with internal resistances \( 4 \, \Omega \) and \( 1 \, \Omega \). What is the equivalent emf?

Q6. A cell of emf \( 6 \, \text{V} \) and internal resistance \( 1.5 \, \Omega \) is connected to a \( 4.5 \, \Omega \) resistor. What is the terminal voltage?

Q7. A wire of length \( 2 \, \text{m} \) and resistance \( 5 \, \Omega \) is stretched to \( 4 \, \text{m} \). What is the new resistance?

Q8. A \( 18 \, \text{V} \) battery with \( 3 \, \Omega \) internal resistance delivers a current of \( 2 \, \text{A} \) to a resistor. What is the resistance of the resistor?

Q9. A wire has a resistance of \( 24 \, \Omega \) at \( 25^\circ \text{C} \) and \( 25.8 \, \Omega \) at \( 75^\circ \text{C} \). What is the temperature coefficient of resistivity?

Q10. A nichrome wire has a resistance of \( 60 \, \Omega \) at \( 25^\circ \text{C} \) and \( \alpha = 1.7 \times 10^{-4} \, ^\circ\text{C}^{-1} \). What is its resistance at \( 225^\circ \text{C} \)?