JEE MainPhysicsCurrent Electricity
A circuit segment consists of a resistor R₁ = 2 k connected in series with a parallel combination of a resistor R₂ = 6 k and an unknown resistor R . This combination is further connected in series with another resistor R₃ = 2 k . The total potential difference across the entire segment is 54 V . If the current flowing through R₂ is 3 mA , the value of the unknown resistor R is
Options
- A3 k
- B2 k
- C6 k
- D9 k
Correct answer
A. 3 k
Step-by-step solution
The voltage drop across the parallel combination is given by Ohm's law applied to R₂ : V_p = I_ R₂ R₂ = 3 mA 6 k = 18 V The remaining voltage drops across the series resistors R₁ and R₃ . The sum of their resistances is R₁ + R₃ = 2 k + 2 k = 4 k . The voltage across the series resistors is: V_ series = V_ total - V_p = 54 V - 18 V = 36 V The total current flowing through the main circuit is: I_ total = V_ series R₁ + R₃ = 36 V 4 k = 9 mA By Kirchhoff's Current Law, the total current splits between R₂ and R . The cu