What will be the impedance of the circuit when resistance (R) and capacitor having capacitance C are connected with AC source of frequency f in series combination :-

Options

A. `sqrt(R+4pi fc^(2))`
B. `sqrt(R+(1)/(2p fc))`
C. `sqrt(R^(2) +(1)/(4pi fc))`
D. `sqrt(R^(2)+(1)/((2pi fc)^(2)))`

Answer

D

Explanation

`Z=sqrt(R^(2)+X_(c)^(2))`
` =sqrt(R^(2)+(1)/(omega^(2)C^(2)))`
` =sqrt(R^(2)+(1)/(4pi ^(2)f^(2)C^(2)))`