In the circuit below, the `AC` source the voltage `V=20cos (omegat)` volts with `omega=2000rad//sec`. The amplitude of the current will be nearest to

Options

A. 2A
B. 3.3A
C. `2 // sqrt(5) A `
D. `sqrt(5) A `

Answer

A

Explanation

`X_(L) = omega L = 2000 xx 5 xx 10 ^(-3) = 10 Omega `
`X_(C) = (1)/(omega C) = (1)/(2000 xx 50 xx 10^(-6)) = 10 Omega `
`Z = sqrt((R_(1) + R_(2))^(2) + (X_(L) - X_(C))^(2)) = sqrt((4 + 6)^(2)) = 10 Omega `
Current (i) ` = (20)/(10) = 2 A `