Capacitor and resistance

Electricity and Magnetism Level 3

given that an ellipsoidal shaped capacitor has its resistance equal to C .. now a resistor of same geometry shape and dimesions is taken .. its resistance R is equal to :-

$conductivity\quad of\quad metal\quad as\quad \sigma \\ permitivity\quad of\quad vaccum\quad as\quad \varepsilon$

\frac { \varepsilon }{ 6\sigma C }

\frac { \varepsilon }{ 2\sigma C }

\frac { \varepsilon \ln { 2 } }{ \sigma C }

\frac { \varepsilon }{ \sigma C }

1 solution

Hemant Khatri
Aug 18, 2014

for any arbitary shaped resistor $R=\frac { \int { E.dr } }{ \sigma \int { E.ds } }$ ..........equation (i) now if we make a capacitor which has same dimensions and geometery we can write C as $C=\frac { (\int { E.ds).\varepsilon \quad } }{ \int { E.dr } }$ .....equation (ii) where c=q/V and using gauss law we get equation (ii) now the integrals formed in both C and R would be same as both have same geometry dimesions etc. thus relating (i) and (ii) we get R= $\frac { \varepsilon }{ C\sigma }$

Nice question...I did by the same way

Kïñshük Sïñgh - 6 years, 9 months ago

Capacitor and resistance

1 solution

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