Physics-
General
Easy

Question

In the capacitor shown in the circuit is changed to 5 V and left in the circuit, in 12s the charge on the capacitor will become left parenthesis e equals 2.718 right parenthesis

  1. fraction numerator 10 over denominator e end fraction C    
  2. fraction numerator e over denominator 10 end fraction C    
  3. fraction numerator 10 over denominator e to the power of 2 end exponent end fraction C    
  4. fraction numerator e to the power of 2 end exponent over denominator 10 end fraction C    

The correct answer is: fraction numerator 10 over denominator e end fraction C


    Final charge on capacitor is
    q equals q subscript 0 end subscript e to the power of negative t divided by R C end exponent
    where q subscript 0 end subscript= charge on capacitor at t equals 0 comma
    R C=time constant of the circuit.
    Putting q subscript 0 end subscript equals C V subscript 0 end subscript
    therefore q equals C V subscript 0 end subscript superscript negative 1 divided by R C end superscript
    Given, C equals 2 F comma V subscript 0 end subscript equals 5 blank v o l t comma R equals 6 blank capital omega comma blank t equals 12 blank s
    Hence, q equals open parentheses 2 cross times 5 close parentheses e to the power of negative left parenthesis 12 divided by 6 cross times 2 right parenthesis end exponent
    equals 10 e to the power of negative 1 end exponent equals fraction numerator 10 over denominator e end fraction C

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