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Physics

The correct formula to calculate the equivalent resistance of two resistors R1 and R2 when connected in parallel, is:

  1. R1+R2R1R2\dfrac{\text R1 + \text R2}{\text R1\text R2} \\[1em]
  2. R1R2R1+R2\dfrac{\text R1\text R2}{\text R1 + \text R2} \\[1em]
  3. R1−R2R1R2\dfrac{\text R1 - \text R2}{\text R1\text R2} \\[1em]
  4. R1R2R1−R2\dfrac{\text R1\text R2}{\text R1 - \text R2} \\[1em]

Current Electricity

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Answer

R1R2R1+R2\dfrac{\text R1\text R2}{\text R1 + \text R2} \\[1em]

Reason — When two resistors are connected in parallel, the potential difference across each resistor is the same, while the current divides between the branches. For two resistors R1 and R2, the reciprocal of the equivalent resistance equals the sum of the reciprocals of the individual resistances i.e.,

1R=1R1+1R2⇒1R=R1+R2R1R2⇒R=R1R2R1+R2\dfrac{1}{\text R} = \dfrac{1}{\text R1} + \dfrac{1}{\text R2} \\[1em] \Rightarrow \dfrac{1}{\text R} = \dfrac{\text R1 + \text R2}{\text R1\text R2} \\[1em] \Rightarrow \text R = \dfrac{\text R1\text R2}{\text R1 + \text R2} \\[1em]

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