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JEE MainPhysicsCurrent Electricity

Three resistors of 6 , 4 , and R are connected in parallel. The total current entering the parallel combination is 6 A . If the power dissipated in the 6 resistor is 24 W , the value of R is ______.

Correct answer

12

Step-by-step solution

Let the currents in the 6 , 4 , and R resistors be I₁ , I₂ , and I₃ respectively. The power dissipated in the 6 resistor is given by P = I₁^2 R₁ . 24 = I₁^2 6 I₁^2 = 4 I₁ = 2 A Since the resistors are in parallel, the potential difference across each resistor is the same. V = I₁ R₁ = 2 6 = 12 V The current through the 4 resistor is: I₂ = V R₂ = 12 4 = 3 A According to Kirchhoff's Current Law, the total current is the sum of the branch currents: I_ total = I₁ + I₂ + I₃ 6 = 2 + 3 + I₃ I₃ = 1 A The value of the unknow

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