Physics-
General
Easy

Question

What is the potential difference between points A a n d B in the circuit shown?

  1. 2 V    
  2. 4 V    
  3. 3 V    
  4. 12 V    

The correct answer is: 2 V


    Consider the charge distribution as shown. Considering the branch on upper side, we have

    fraction numerator q over denominator V subscript x end subscript minus V subscript A end subscript end fraction equals 4 cross times 10 to the power of negative 6 end exponent
    fraction numerator q over denominator V subscript A end subscript minus V subscript y end subscript end fraction equals blank 2 cross times 10 to the power of negative 6 end exponent
    Here, V subscript x end subscript equals 6 blank v o l t comma blank V subscript y end subscript equals 0
    therefore fraction numerator q over denominator 6 minus V subscript A end subscript end fraction equals 4 cross times 10 to the power of negative 6 end exponent…(i)
    fraction numerator q over denominator V subscript A end subscript minus 0 end fraction equals 2 cross times 10 to the power of negative 6 end exponent …(ii)
    From Eqs. (i) and (ii), we get
    fraction numerator V subscript A end subscript over denominator 6 minus V subscript A end subscript end fraction equals 2
    therefore V subscript A end subscript equals 4 v o l t
    Similarly for the lower side branch
    fraction numerator q ´ ´ over denominator 6 minus V subscript B end subscript end fraction equals blank 2 cross times 10 to the power of negative 6 end exponent…(iii)
    fraction numerator q ´ ´ over denominator V subscript B end subscript minus 0 end fraction equals blank 4 cross times 10 to the power of negative 6 end exponent...(iv)
    From Eqs. (iii) and (iv)
    fraction numerator V subscript B end subscript over denominator 6 minus V subscript B end subscript end fraction equals fraction numerator 1 over denominator 2 end fraction
    therefore blank V subscript B end subscript equals 2 blank v o l t
    therefore V subscript A end subscript minus V subscript B end subscript equals 4 minus 2 equals 2 blank v o l t

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