NEET Current Electricity — Set 18

Question 1

In a circuit, a $ 20 \, \text{V} $ battery with negligible internal resistance is connected across a cubical network of 12 resistors, each $ 2 \, \Omega $. What is the total current?

Accepted Answer

Equivalent resistance of cube network: $ R_{\text{eq}} = \frac{5}{6} R = \frac{5}{6} \times 2 = \frac{10}{6} = \frac{5}{3} \, \Omega $. Total current: $ I = \frac{V}{R_{\text{eq}}} = \frac{20}{\frac{5}{3}} = 20 \times \frac{3}{5} = 12 \, \text{A} $.

Question 2

A circuit has a $ 8 \, \text{V} $ battery with $ 2 \, \Omega $ internal resistance and two resistors $ 4 \, \Omega $ and $ 4 \, \Omega $ in parallel. What is the total current?

Accepted Answer

Parallel resistance: $ \frac{1}{R_p} = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = 0.5 \Rightarrow R_p = 2 \, \Omega $. Total resistance: $ R_{\text{total}} = 2 + 2 = 4 \, \Omega $. Current: $ I = \frac{\varepsilon}{R_{\text{total}}} = \frac{8}{4} = 2 \, \text{A} $.

Question 3

A wire has a resistance of $ 35 \, \Omega $ at $ 20^\circ \text{C} $ and $ 36.4 \, \Omega $ at $ 60^\circ \text{C} $. What is the temperature coefficient of resistivity?

Accepted Answer

Use: $ R_t = R_0 [1 + \alpha (T - T_0)] $. Substitute: $ 36.4 = 35 [1 + \alpha (60 - 20)] $. Solve: $ 36.4 = 35 + 1400\alpha \Rightarrow 1400\alpha = 1.4 \Rightarrow \alpha = \frac{1.4}{1400} = 1.0 \times 10^{-3} \, ^\circ\text{C}^{-1} $.

NEET Physics: Current Electricity — Practice Set 18

Q1. In a circuit, a \( 20 \, \text{V} \) battery with negligible internal resistance is connected across a cubical network of 12 resistors, each \( 2 \, \Omega \). What is the total current?

Q2. A circuit has a \( 8 \, \text{V} \) battery with \( 2 \, \Omega \) internal resistance and two resistors \( 4 \, \Omega \) and \( 4 \, \Omega \) in parallel. What is the total current?

Q3. A wire has a resistance of \( 35 \, \Omega \) at \( 20^\circ \text{C} \) and \( 36.4 \, \Omega \) at \( 60^\circ \text{C} \). What is the temperature coefficient of resistivity?

Q4. A \( 9 \, \text{V} \) battery with \( 0.5 \, \Omega \) internal resistance is connected to a \( 8.5 \, \Omega \) resistor. What is the power dissipated in the external resistor?

Q5. Two cells of emf \( 5 \, \text{V} \) and \( 7 \, \text{V} \) with internal resistances \( 2 \, \Omega \) and \( 4 \, \Omega \) are connected in series with a \( 6 \, \Omega \) resistor. What is the current through the circuit?

Q6. A \( 30 \, \text{V} \) battery with negligible internal resistance is connected to a cubical network of 12 resistors, each \( 5 \, \Omega \). What is the total current?

Q7. A wire of length \( 10 \, \text{m} \) and cross-sectional area \( 1 \times 10^{-6} \, \text{m}^2 \) has a resistance of \( 20 \, \Omega \). What is the resistivity of the material?

Q8. A \( 12 \, \text{V} \) battery with \( 2 \, \Omega \) internal resistance is connected to a \( 10 \, \Omega \) resistor. What is the power dissipated in the internal resistance?

Q9. Two cells of emf \( 5 \, \text{V} \) and \( 9 \, \text{V} \) with internal resistances \( 1 \, \Omega \) and \( 2 \, \Omega \) are connected in series with a \( 7 \, \Omega \) resistor. What is the current through the circuit?

Q10. A \( 8 \, \Omega \) resistor carries a current of \( 2.5 \, \text{A} \) for \( 10 \, \text{s} \). What is the energy dissipated?