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Question
L, C and R represent the physical quantities inductance, capacitance and resistance respectively. Which of the following combinations have dimensions of frequency?
(a) `1/(RC)`
(b) `R/L`
(c) `1/sqrt(LC)`
(d) C/L
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Solution
(a) `1/(RC)`
(b) `R/L`
(c) `1/sqrt(LC)`
The time constant of the RC circuit is given by
`tau=RC`
On taking the reciprocal of the above relation, we get
`f_1=1/(RC).............(1)`
f1 will have the dimensions of the frequency.
The time constant of the LR circuit is given by
`tau=L/R`
On taking the reciprocal of the above relation, we get
`f_2=R/L............(2)`
f2 will have the dimensions of the frequency.
On multiplying eq. (1) and (2), we get
`f_1f_2=1/(LC)`
`rArrsqrt(f_1f_2)=1/sqrt(LC)`
Thus, `sqrt(f_1f_2)` will have the dimensions of the frequency.
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