A conducting medium is shaped in a form of a quarter of an annulus of radii $b$ and $a$ $(b > a)$ and thickness $t$ . Specific resistance of the medium is $ρ$ .The correct option(s) is (are)

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Resistance between LMNO and PQRS is $\frac{2 ρ}{πt} In (\frac{b}{a})$

Resistance between LMRS and ONQP is $\frac{πρ}{2t In (\frac{b}{a})}$

Resistance between MRQN and LSPO is $\frac{4ρt}{π (b^{2} {-a}^{2})}$

Resistance between faces LMNO and PQRS and also between faces LMRS and ONQP is same

answer is A, B, C.

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Detailed Solution

Between LMNO and PQRS
$\int dR = R_{eq} = \frac{2 ρ}{πt} \int_{a}^{b} \frac{dr}{r}$
$∴ R_{eq} = \frac{2 ρ}{πt} \ln (\frac{b}{a})$
Between LMRS and ONQP is
$\frac{1}{R_{eq}} = \int \frac{1}{dR} = \frac{2 t}{πρ} \int \frac{dr}{r} ∴ \frac{1}{R_{eq}} = \frac{2 t}{πρ} \ln (\frac{b}{a})$
$∴ R_{eq} = \frac{πρ}{2 tln (\frac{b}{a})}$
Between MRQN and LSPO
$R_{eq} = \frac{4 ρt}{π (b^{2} - a^{2})}$