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 `0.4A` .
B. the current through the circuit `I` is `0.3sqrt2A` .
C. the voltage across `100 Omega` resistor `= 10 sqrt2V` .
D. the voltage across `50 Omega` resistor `=10V` .

Answer

C

Explanation

`R -C` circuit
`Z = sqrt(R^(2) + X_(c)^(2)) = sqrt((100)^(2) + ((1)/(100 xx 100 xx 10^(-6)))^(2))`
`=sqrt((100)^(2) + (100)^(2)) = 100 sqrt2 Omega`
Current in this branch `i_(1) = (20)/(100 sqrt2) = (1)/(5 sqrt2)A`
Current leads voltage `(tan phi = X_(C)/(R) = 1)by pi/4`
`R` -Lcircuit
`Z' = sqrt(R^(2) + X_(L)^(C)) = sqrt((50)^(2) + (100xx 5)^(2)) = 50sqrt2 Omega`
Current lags the voltage by `(tan phi ' = (X_(L))/(R) =1)by (pi)/(4)`
Resultant current
`i = sqrt(((1)/(5sqrt2))^(2) + ((2)/(5sqrt2))^(2))`
p .d across `100 Omega, V_(1) = i_(1) xx 100 = (1)/(sqrt2 xx 100 = 10sqrtV`
p.d across `50 Omega, V_(2) = i_(2) xx 50 = (2)/(5 sqrt2) xx 50 = 10sqrt2V`