Physics-
General
Easy

Question

In a network as shown in the figure, the potential difference across the resistance 2R is (the cell has an emf of E volt and has no ingternal resistance)

  1. 2E    
  2. fraction numerator 4 E over denominator 7 end fraction    
  3. fraction numerator E over denominator 7 end fraction    
  4. E    

The correct answer is: fraction numerator 4 E over denominator 7 end fraction


    In the given circuit, resistors 4R and 2R are connected in parallel while resistance R is connected in series to it.
    Hence, equivalent resistance is

    fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator 4 R end fraction plus fraction numerator 1 over denominator 2 R end fraction
    equals fraction numerator 6 R over denominator 8 R to the power of 2 end exponent end fraction
    R to the power of ´ end exponent equals fraction numerator 8 over denominator 6 end fraction R
    equals fraction numerator 4 over denominator 3 end fraction R
    ⟹ R to the power of ´ ´ end exponent equals R plus fraction numerator 4 over denominator 3 end fraction R equals fraction numerator 7 R over denominator 3 end fraction
    Given, emf is E volts, therefore
    i equals fraction numerator E over denominator R end fraction equals fraction numerator 3 E over denominator 7 R end fraction

    Potential difference across R is
    V equals i r equals fraction numerator 3 R over denominator 7 R end fraction cross times R equals fraction numerator 3 E over denominator 7 end fraction
    Potential difference across 2R is
    V to the power of ´ end exponent equals E minus fraction numerator 3 E over denominator 7 end fraction equals fraction numerator 4 E over denominator 7 end fraction

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