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JEE MainPhysicsCurrent Electricity

A circuit consists of a battery of unknown voltage V connected in series with a resistor R₁ = 4 , which then splits into two parallel branches containing resistors R₂ = 6 and R₃ = 3 . The parallel branches reconnect and are connected in series with a resistor R₄ = 2 back to the battery. If the current flowing through the resistor R₃ is 2 A , the voltage V of the battery is:

Options

  1. A16 V
  2. B24 V
  3. C12 V
  4. D20 V

Correct answer

B. 24 V

Step-by-step solution

The voltage drop across the parallel combination is equal to the voltage drop across R₃ : V_p = I₃ R₃ = 2 3 = 6 V The current through R₂ is: I₂ = V_p R₂ = 6 6 = 1 A The total current drawn from the battery is: I_ total = I₂ + I₃ = 1 + 2 = 3 A The equivalent resistance of the parallel combination of R₂ and R₃ is: R_p = 6 3 6 + 3 = 2 The total equivalent resistance of the circuit is: R_ eq = R₁ + R_p + R₄ = 4 + 2 + 2 = 8 The voltage of the battery is: V = I_ total R_ eq = 3 8 = 24 V Answer: 24 V

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