The impedance of a R.C circuit is `Z_1` for frequency f and `Z_2` for frequency 2f. Then, `Z_1//Z_2` is

Options

A. a)between 1 and 2
B. b)2
C. c) 4 `
D. `d)1/2`

Answer

A

Explanation

The impedance of R-C circuit for frequency `f_1` is
`Z_1=sqrt(R^2+1/(4 pi^2f^2C^2))`
The impedance of R-C circuit for frequency 2f is
`Z_2=sqrt(R^2+1/(4 pi ^2(2f^2)C^2))`
or `Z_2=sqrt(R^2+1/(4 pi^2(2f^2)C^2))`
THen, `Z_1^2/Z_2^2= (R^2+1/(4 pi^2 f^2C^2))/(R^2+ 1/(16pi^2f^2C^2))`
or `Z_1^2/Z_2^2= (1 +1/(4 pi^2 f^2 C^2 R^2))/(1+1/(16 pi^2f^2 R^2 C^2))`
value is greater than 1,
Hence, `Z_1/Z_2`=lies between 1 and 2.