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BITSAT2023PhysicsMathematics in PhysicsActual

Two resistances are given as R₁=(10 0.5) and R₂=(15 0.5) . The percentage error in the measurement of equivalent resistance when they are connected in parallel is

Options

  1. A6.33
  2. B2.33
  3. C4.33
  4. D5.33

Correct answer

C. 4.33

Step-by-step solution

Equivalent resistance in parallel combination is given by aligned & 1 R_ eq = 1 R₁ + 1 R₂ & R_ eq = R₁ R₂ R₁+R₂ = 10 15 10+15 =6 aligned Differentiating both sides, we get aligned & R_ eq R _ eq ^2 = R ₁ R ₁^2 + R ₂ R ₂^2 & R _ eq R _ eq = ( R ₁ R ₁^2 + R ₂ R ₂^2 ) R _ eq & = ( 0.5 100 + 0.5 225 ) 6= ( 6 0.5 25 ) ( 1 4 + 1 9 )= 13 300 & R _ eq R _ eq 100= 13 3 =4.33 % aligned

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