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Unit of (CV)/(rho epsilon(0)) are of (...

Unit of `(CV)/(rho epsilon_(0))` are of
(`C =` capacitance, `V =` potential, `rho =` specfic resistence and `epsilon_(0) =` permittivity of free space)`

Text Solution

Verified by Experts

The correct Answer is:
1
Here, `C =(q)/(V) = (q)/(W//q) = (q^2)/(W) = ((AT)^2)/(ML^2 T^(-2))`
`[M^(-1) L^(-2) T^4 A^2]`
`V = [ML^2 T^(-3) A^(-1)]`
`rho = (Ra)/(I) = (V)/(I) (a)/(I) = ((ML^2 T^(-3) A^(-1))(L^2))/(AL)`
`=[ML^3 T^(-3) A^(-2)]`
From `F = (q_1 q_2)/(4 pi in_0 r^2)`
`"in"_0 = (q_1q_2)/(4pi F r^2) = ((AT)^2)/((MLT)^(-2) (L^2)) = [M^(-1) L^(-3) T^4 A^2]`
Now, `(CV)/(rho "in"_0) = (q)/(rho "in"_0)`
`=(AT)/((ML^3 T^(-3)) (M^(-1) L^(-3) T^4 A^2))`
= [A]
:. dimension of A = 1
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