An AC source producing `emf`
`epsilon = epsilon_0 [cos(100 pi s^(-1)) t + cos (500 pi s^(-1))t]`
is connected in series with a capacitor and a resistor. The steady-state current in the circuit is found to be
`I = i_1 cos [(100 pi s^(-1) t + varphi_1] + i_2 cos [(500 pi s^(-1))t +phi_2]`.

Options

A. `i_(1)gti_(2)`
B. `i_(1) =i_(2)`
C. `i_(1)lt i_(2)`
D. none

Answer

C

Explanation

Impedance of `RC` circuit
`Z = sqrt(R^(2) + ((1)/(omegaC))^(2)`
`i_(1) = (E_(0))/(sqrt(R^(2) + ((1)/(100piC))^(2))) i_(2) = (E_(0))/(sqrt(R^(2) + ((1)/(500 pi C))^(2)))`
`i_(1) lt i_(2)` .