A 100pF capacitor is charged to apotential difference of 24V.it is connected to an uncharged capicitor of capacitance
20uF. What  will be the new potential difference across the 100pF capacitor.

Asked by Amrit | 16th May, 2015, 03:48: PM

Expert Answer:

begin mathsize 14px style Given colon straight C subscript 1 equals 100 space pF space equals space 100 space cross times space 10 to the power of negative 12 end exponent space straight F straight V subscript 1 equals space 24 space straight V Energy space stored space in space the space capacitor comma straight U subscript 1 equals 1 half straight C subscript 1 straight V subscript 1 equals 1 half cross times 100 space cross times space 10 to the power of negative 12 end exponent space cross times open parentheses 24 close parentheses squared space space space space space space space space space space space space space space space space space space space space equals space 50 space cross times space 10 to the power of negative 12 end exponent space cross times space 576 space space space space space space space space space space space space space space space space space space space space equals space 28800 space cross times space 10 to the power of negative 12 end exponent space straight J When space this space charged space capacitor space is space connected space to space another space uncharged space capacitor space straight C subscript 2 space equals space 20 space pF comma space they space will space share space charges comma space till space the space potential space differences space accross space their space plates space become space equal. straight C subscript 2 space equals space 20 space pF space equals 20 space cross times space 10 to the power of negative 12 end exponent space straight F straight V subscript 2 equals 0 Total space charge space on space the space two space capacitors comma straight q equals space straight C subscript 1 straight V subscript 1 space plus straight C subscript 2 straight V subscript 2 space space space space space space space space space space space space equals space 100 space cross times space 10 to the power of negative 12 end exponent space cross times space 24 space plus space 20 space cross times space 10 to the power of negative 12 end exponent space cross times space 0 space space equals space 2400 space cross times space 10 to the power of negative 12 end exponent space straight C Total space capacitance space of space the space two space capacitors comma straight C space equals space straight C subscript 1 space plus space straight C subscript 2 space equals space 100 space pF space plus space 20 space pF space equals space 120 space pF Therefore comma space potential space stored space of space the space two space capacitors comma straight V equals straight q over straight C equals fraction numerator 2400 space cross times space 10 to the power of negative 12 end exponent over denominator 120 space cross times 10 to the power of negative 12 end exponent end fraction equals 20 space straight V end style

Answered by Faiza Lambe | 18th May, 2015, 12:13: PM

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