In the given circuit, the AC source has `(omega) = 100 rad//s`. Considering the inductor and capacitor to be ideal, the correct choice(s) is (are)
.

Options

A. The current through the circuit , I is 0.3 A
B. The current through the circuit , I is 0.3`sqrt 2` A
C. The voltage across `100Omega` resistor = 10`sqrt 2`V
D. The voltage across `50 Omega` resistor = 10 V

Answer

A, C, D

Explanation

`X_L = omegaL = 10 xx 0.5 = 50Omega`
`X_C = 1/omegaC = 1/100 xx 100cc 10^(-6) = 100Omega`
`Z_1 = 100sqrt 2, I_1 = 20/sqrt 100sqrt 2 = 1/5sqrt 2`
V across `100 Omega` = `1/5sqrt 2 xx 100 = 20/sqrt 2 xx sqrt 2/sqrt 2` = `10sqrt 2` V
Phase difference between `I_1` and V, cos`phi_1` = `R_1/Z_1 = 100 / 100sqrt 2`
`implies phi = pi`/4
Therefore, `I_1` lead V
`Z_2 = 50sqrt 2 , I_2 = 20/50sqrt 2 = 2/5sqrt 2` A
V across `50Omega = 2/50sqrt 2xx 50 = 20/sqrt 2 = 10sqrt 2 V impliesphi_2= pi/4`
`I_2` lag V by `pi/4`
`impliesI_Net = sqrt (I_1^(2) + I_(2)^(2))`
I = `sqrt ( 1 / 25 xx 2 + 2 / 25 xx 2) = sqrt 5/50 = 1 / sqrt 10 implies I = 0.316` A