In the circuit shown in the figure, the a.c. source gives a voltage V=20 cos (2000t). Neglecting source resistance, the voltmeter and ammeter reading will be

Options

A. 1.68 V, 0.47A
B. 0V, 0.47A
C. 5.6 V, 1.4 A
D. 0V, 1.4 A

Answer

C

Explanation

V=20cos(2000t)
`therefore`Peak value of the
a.c. voltage=20V.
`thereforeV_(r.m.s)=(20)/(sqrt(2))V`.
and frequency f is given
by `2pif=2000`.
Inductive reactance of the coil`=X_(L)=omegaL=2pifL`
`=2000xx5xx10^(-3)=10Omega`.
Capacitance reactance`=X_(C)=(1)/(2pifC)`
`=(1)/(2000xx50xx10^(-6))=10Omega`.
The given circuit is a R-L-C series circuit.
`therefore` Impendence`=Z=sqrt(R^(2)+(X_(L)-X_(C))^(2))`
`=sqrt(10^(2)+(10-10)^(2))=10Omega`
`therefore`Current, `I=(V_(r.m.s))/(Z)=(20//sqrt(2))/(10)=sqrt(2)`
`=1.41cong1.4` amp.
Voltage difference across the coil and the capacitance
`=Ixxsqrt(4^(2)+(10-10)^(2))=sqrt(2)xx4=5.6V`
`therefore`The voltmeter and ammeter reading will be 5.6 V and 1.4 A respectively.