The plates of a parallel plate capacitor are charged upto 100V.A 2mm thick plate is inserted between the plates then to maintain the same potential difference,the distance between the plates is increased by 1.6mm.Then what is the dielectric constant of the plate??

Asked by Malavika Umesh | 16th May, 2015, 10:01: AM

Expert Answer:

Given that the parallel plate capacitors are charged to 100 V
Thickness of the plate, t = 2 mm
begin mathsize 14px style The space potential space difference space between space the space plates space with space air space as space the space dieletrics space is colon straight V subscript air space equals fraction numerator straight Q over denominator straight epsilon subscript 0 straight A end fraction straight d straight V subscript air space equals straight sigma over straight epsilon subscript 0 straight d In space the space presence space of space straight a space medium comma space the space potential space difference space between space the space plates space will space be colon straight V subscript medium equals fraction numerator straight Q over denominator straight epsilon subscript 0 straight A end fraction open square brackets straight d minus straight t plus straight t over straight K close square brackets straight V subscript medium equals straight sigma over straight epsilon subscript 0 open square brackets straight d minus straight t plus straight t over straight K close square brackets Potential space difference space between space the space plates space with space dielectrics space and space increased space distance space is colon straight V subscript medium apostrophe equals straight sigma over straight epsilon subscript 0 open square brackets open parentheses straight d plus straight d apostrophe close parentheses minus straight t plus straight t over straight K close square brackets It space is space given space that colon straight V subscript air space equals straight V subscript medium apostrophe straight sigma over straight epsilon subscript 0 straight d equals straight sigma over straight epsilon subscript 0 open square brackets open parentheses straight d plus straight d apostrophe close parentheses minus straight t plus straight t over straight K close square brackets straight d equals open parentheses straight d plus straight d apostrophe close parentheses minus straight t plus straight t over straight K straight d apostrophe equals 1.6 mm straight t equals 2 space mm straight d equals open parentheses straight d plus straight d apostrophe close parentheses minus straight t plus straight t over straight K straight d equals open parentheses straight d plus 1.6 close parentheses minus 2 plus 2 over straight K 2 equals 1.6 plus 2 over straight K 0.4 equals fraction numerator 2 space over denominator straight K end fraction straight K equals 5 end style
The dielectric constant of the plate ,K =5

Answered by Jyothi Nair | 18th May, 2015, 10:47: AM