NEET Current Electricity — Set 3

Question 1

A $ 6 \, \text{V} $ battery with $ 0.5 \, \Omega $ internal resistance is connected to a $ 5.5 \, \Omega $ resistor. What is the power dissipated in the external resistor?

Accepted Answer

Total resistance: $ R_{\text{total}} = 5.5 + 0.5 = 6 \, \Omega $. Current: $ I = \frac{\varepsilon}{R_{\text{total}}} = \frac{6}{6} = 1 \, \text{A} $. Power: $ P = I^2 R = 1^2 \times 5.5 = 5.5 \, \text{W} $.

Question 2

A $ 18 \, \text{V} $ battery with negligible internal resistance is connected to a $ 6 \, \Omega $ and $ 12 \, \Omega $ resistor in series. What is the power dissipated in the $ 6 \, \Omega $ resistor?

Accepted Answer

Total resistance: $ R = 6 + 12 = 18 \, \Omega $. Current: $ I = \frac{V}{R} = \frac{18}{18} = 1 \, \text{A} $. Power: $ P = I^2 R = 1^2 \times 6 = 6 \, \text{W} $.

Question 3

A circuit has a $ 28 \, \text{V} $ battery with $ 4 \, \Omega $ internal resistance and three resistors $ 4 \, \Omega $, $ 8 \, \Omega $, $ 16 \, \Omega $ in parallel. What is the current through the $ 8 \, \Omega $ resistor?

Accepted Answer

Parallel resistance: $ \frac{1}{R_p} = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} = \frac{4 + 2 + 1}{16} = \frac{7}{16} \Rightarrow R_p = \frac{16}{7} \approx 2.29 \, \Omega $. Total resistance: $ R_{\text{total}} = 4 + 2.29 = 6.29 \, \Omega $. Total current: $ I = \frac{\varepsilon}{R_{\text{total}}} = \frac{28}{6.29} \approx 4.45 \, \text{A} $. Voltage across parallel: $ V = I R_p = 4.45 \times 2.29 \approx 10.19 \, \text{V} $. Current through $ 8 \, \Omega $: $ I_8 = \frac{V}{8} = \frac{10.19}{8} \approx 1.27 \, \text{A} $.

NEET Physics: Current Electricity — Practice Set 3

Q1. A \( 6 \, \text{V} \) battery with \( 0.5 \, \Omega \) internal resistance is connected to a \( 5.5 \, \Omega \) resistor. What is the power dissipated in the external resistor?

Q2. A \( 18 \, \text{V} \) battery with negligible internal resistance is connected to a \( 6 \, \Omega \) and \( 12 \, \Omega \) resistor in series. What is the power dissipated in the \( 6 \, \Omega \) resistor?

Q3. A circuit has a \( 28 \, \text{V} \) battery with \( 4 \, \Omega \) internal resistance and three resistors \( 4 \, \Omega \), \( 8 \, \Omega \), \( 16 \, \Omega \) in parallel. What is the current through the \( 8 \, \Omega \) resistor?

Q4. A circuit has a \( 16 \, \text{V} \) battery with \( 2 \, \Omega \) internal resistance and three resistors \( 2 \, \Omega \), \( 4 \, \Omega \), \( 8 \, \Omega \) in parallel. What is the current through the \( 2 \, \Omega \) resistor?

Q5. A wire of length \( 3 \, \text{m} \) and cross-sectional area \( 3 \times 10^{-6} \, \text{m}^2 \) has a resistance of \( 5 \, \Omega \). What is the resistivity of the material?

Q6. A cell of emf \( 7 \, \text{V} \) and internal resistance \( 1 \, \Omega \) is connected to a \( 6 \, \Omega \) resistor. What is the terminal voltage?

Q7. A \( 10 \, \text{V} \) battery with \( 1 \, \Omega \) internal resistance is connected to a \( 9 \, \Omega \) resistor. What is the power dissipated in the internal resistance?

Q8. In a circuit with two resistors of different resistances in series, which resistor dissipates more power if the same current flows through both?

Q9. Two cells of emf \( 2.5 \, \text{V} \) and \( 3.5 \, \text{V} \) with internal resistances \( 0.5 \, \Omega \) and \( 1 \, \Omega \) are connected in series. What is the equivalent emf?

Q10. A \( 5 \, \Omega \) resistor carries a current of \( 2 \, \text{A} \) for \( 10 \, \text{s} \). How much energy is dissipated as heat?