If various elements, i.e., resistance capacitance and inductance which are in series and having values `1000 Omega, 1 mu F` and `2.0 H` respectively. Given emf as, `V = 100 sqrt(2) sin 1000 t` volts
Voltage across the resistor is

Options

A. 70.7 Volts
B. 100 Volts
C. 141.4 Volts
D. 270.7 Volts

Answer

A

Explanation

rms value of voltage across the source
`V_("rms") = (100 sqrt(2))/(sqrt(2)) = 100` volt
From question, `omega = 1000 "rad"//s`
`i_("rms") = (V_("rms"))/(|Z|) = (V_("rms"))/(sqrt(R^(2) + (X_(L) - X_(C ))^(2)))`
`= (V_("rms"))/(sqrt(R^(2) + (omega L - (1)/(omega C))^(2)))`
`= (100)/(sqrt((1000)^(2) + (1000 xx 2 - (1)/(1000 x 1 xx 10^(-6)))^(2)))`
= 0.0707 amp
Since the current will be same every where in the circuit, therefore
`P.D` acrossresistor
`V_(R ) = i_("rms")R = 0.0707 xx 1000 = 70.7` volts