CBSE Class 12-science Answered

The plates of a parallel plate capacitor have an area of 90 cm² each and are separated by 2.5 mm The capacitor is charged by connecting it to a 400 V supply How much electrostatic energy is stored by the capacitor? View this energy as stored in the electrostatic field between the plates, and obtain the energy per unit volume u. Hence arrive at a relation between u and the magnitude of electric field E between the plates.

Asked by Topperlearning User | 22 Apr, 2015, 09:59: AM

Expert Answer

Area of the plates of a parallel plate capacitor, A = 90 cm² = 90 x 10^-4m² Distance between the plates, d = 2.5 mm = 2.5 x 10^-3 m potential difference across the plates, V = 400 V

Capacitance of the capacitor is given by the relation,

$begin mathsize 11px style straight C equals fraction numerator element of subscript 0 straight A over denominator straight d end fraction end style$

Electrostatic energy stored in the capacitor is given by the relation, $begin mathsize 11px style straight E subscript 1 equals 1 half CV squared end style$

$begin mathsize 11px style equals 1 half fraction numerator element of subscript 0 straight A over denominator straight d end fraction straight v squared end style$

Where,

$Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.$ = Permittivity of free space = 8.85 x 10^-12C²N^-1m^-2

$begin mathsize 11px style straight E subscript 1 equals fraction numerator 1 cross times space 8.85 space cross times space 10 to the power of negative 12 end exponent space cross times space 90 space straight x 10 to the power of negative 4 end exponent space cross times space left parenthesis 400 right parenthesis squared over denominator 2 space cross times space 2.5 space cross times space 10 to the power of negative 3 end exponent end fraction equals space 2.55 space cross times space 10 to the power of negative 6 end exponent straight J end style$

Hence, the electrostatic energy stored by the capacitor is 2.55 x 10^-6J

(b) Volume of the given capacitor,

V' = A x d

= 90 x 10^-4 x 2.5 x 10^-3

= 2.25 x 10^-5m³

Energy stored in the capacitor per unit volume is given by,

$begin mathsize 12px style u equals fraction numerator E subscript 1 over denominator V apostrophe end fraction space space space equals fraction numerator 2.55 space x space 10 to the power of negative 6 end exponent over denominator 2.25 space x space 10 to the power of negative 4 end exponent end fraction equals 0.0113 space Jm to the power of negative 3 end exponent end style$

Again, $begin mathsize 11px style straight u fraction numerator straight E subscript 1 over denominator straight V apostrophe end fraction end style$

$begin mathsize 11px style equals fraction numerator begin display style 1 half CV squared end style over denominator Ad end fraction equals fraction numerator begin display style fraction numerator element of subscript 0 straight A over denominator 2 straight d end fraction end style over denominator Ad end fraction equals 1 half element of subscript 0 open parentheses straight V over straight d close parentheses squared end style$