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What is the capacitance of a 1 m long hifi cable where the central conductor is 1 mm in diameter and the shield is 5 mm in diameter?

1 Answer

Here $C=?,L=1m$
$r_a=\large\frac{1}{2}$$ mm=0.5 mm= 5 \times 10^{-4} m$
$r_b=\large\frac{5}{2}$$ mm=2.5 mm=2.5 \times 10^{-3} m$
For a cylindrical capacitor.
$C= \large\frac{2 \pi \in_0 L}{\log_e \bigg( \Large\frac{r_a}{r_b} \bigg) }$
$\quad= \large\frac{4 \pi \in_0 L}{2 \log _e (r_a/r_b)}$
$\quad= \large\frac{1 \times 1}{9 \times 10^3 \times 2 \log_e \bigg( \Large\frac{2.5 \times 10^{-3}}{5 \times 10^{-4}} \bigg)}$
$\quad= 3.45 \times 10^{-11}F$
$\quad= 34.5 \times 10^{-12} F= 34.5 pF$
Hence B is the correct answer.
answered Jun 13, 2014 by meena.p

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