NEET Current Electricity — Set 14

Question 1

In a circuit with a variable resistor, under what condition is the power delivered to the resistor maximized?

Accepted Answer

Power $ P = I^2 R = (\varepsilon / (R + r))^2 R $. Maximum power transfer occurs when $ R = r $ (internal resistance), balancing current and resistance for optimal energy delivery.

Question 2

A circuit has a $ 9 \, \text{V} $ battery with $ 1 \, \Omega $ internal resistance and two resistors $ 5 \, \Omega $ and $ 3 \, \Omega $ in parallel. What is the total current?

Accepted Answer

Parallel resistance: $ \frac{1}{R_p} = \frac{1}{5} + \frac{1}{3} = \frac{3 + 5}{15} = \frac{8}{15} \Rightarrow R_p = \frac{15}{8} = 1.875 \, \Omega $. Total resistance: $ R_{\text{total}} = 1 + 1.875 = 2.875 \, \Omega $. Current: $ I = \frac{\varepsilon}{R_{\text{total}}} = \frac{9}{2.875} \approx 3.13 \, \text{A} $.

Question 3

A $ 40 \, \text{V} $ battery with negligible internal resistance is connected to a cubical network of 12 resistors, each $ 4 \, \Omega $. What is the total current?

Accepted Answer

Equivalent resistance: $ R_{\text{eq}} = \frac{5}{6} R = \frac{5}{6} \times 4 = \frac{20}{6} \approx 3.33 \, \Omega $. Total current: $ I = \frac{V}{R_{\text{eq}}} = \frac{40}{\frac{20}{6}} = 40 \times \frac{6}{20} = 12 \, \text{A} $.

NEET Physics: Current Electricity — Practice Set 14

Q1. In a circuit with a variable resistor, under what condition is the power delivered to the resistor maximized?

Q2. A circuit has a \( 9 \, \text{V} \) battery with \( 1 \, \Omega \) internal resistance and two resistors \( 5 \, \Omega \) and \( 3 \, \Omega \) in parallel. What is the total current?

Q3. A \( 40 \, \text{V} \) battery with negligible internal resistance is connected to a cubical network of 12 resistors, each \( 4 \, \Omega \). What is the total current?

Q4. A circuit has a \( 12 \, \text{V} \) battery with \( 3 \, \Omega \) internal resistance and two resistors \( 6 \, \Omega \) and \( 3 \, \Omega \) in parallel. What is the total current?

Q5. A Wheatstone bridge has \( R_1 = 22 \, \Omega \), \( R_2 = 44 \, \Omega \), \( R_3 = 15 \, \Omega \). What is \( R_4 \) for balance?

Q6. Why does a semiconductor’s resistance decrease with increasing temperature, unlike a metal?

Q7. A circuit with a \( 9 \, \text{V} \) battery and \( 1 \, \Omega \) internal resistance has three resistors: \( 2 \, \Omega \), \( 3 \, \Omega \), and \( 6 \, \Omega \) in parallel. What is the total current drawn from the battery?

Q8. In a conductor, if the number of free electrons per unit volume doubles while the electric field and relaxation time remain constant, what happens to the current density?

Q9. A \( 15 \, \text{V} \) battery with negligible internal resistance is connected to a \( 5 \, \Omega \) and \( 10 \, \Omega \) resistor in series. What is the power dissipated in the \( 5 \, \Omega \) resistor?

Q10. A \( 36 \, \text{V} \) battery with negligible internal resistance is connected to a cubical network of 12 resistors, each \( 6 \, \Omega \). What is the total current?