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what is the capacitance of a 1m long hi...

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

Text Solution

Verified by Experts

Here, `C = ?, L = 1m`
`r_(a) = (1)/(2) mm = 0.5mm = 5xx10^(-4) m`,
`r_(b) = (5)/(2) mm = 2.5 mm = 2.5xx10^(-3)m`
For a cylindrical capacitor,
`C = (2pi in_(0) L)/(log_(e) (r_(b)/(r_(a)))) = (4pi in_(0) L)/(2log_(e) (r_(b)//r_(a)))`
`= (1xx1)/(9xx10^(9)xx2 log_(e) ((2.5xx10^(-3))/(5xx10^(-4))))`
`C = (1)/(18xx10^(9) log_(e) 5) = (10^(-9))/(18xx1.609)`
`3.45xx10^(-11) F = 34.5 pF`
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