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JEE Main 2004 (AIEEE) · Combination of Resistors

Combination of Resistors question from JEE Main 2004 (AIEEE)

Q77JEE Main 2004 · AIEEEMedium

Combination of Resistors

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of 43\frac{4}{3} and 23\frac{2}{3}, then the ratio of the current passing through the wires will be

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Answer: (b)

  1. R=ρlπr2R = \dfrac{\rho l}{\pi r^2}, so R1R2=l1l2⋅r22r12=43×94=3\dfrac{R_1}{R_2} = \dfrac{l_1}{l_2} \cdot \dfrac{r_2^2}{r_1^2} = \dfrac{4}{3} \times \dfrac{9}{4} = 3.
  2. In parallel I∝1RI \propto \dfrac{1}{R}: I1I2=R2R1=13\dfrac{I_1}{I_2} = \dfrac{R_2}{R_1} = \dfrac{1}{3}
  3. So the answer is (b) 1/31/3.
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