An alternating voltage. `V=6sin20t+8cos20t` is applied to a series resonant circuit as shown. The correct statement (s) is/are

Options

A. The capacitance C is 12.5 mF
B. The rms current in the circuit is 2A
C. The power dissipated in the circuit is 10W.
D. The quality factor of the circuit is 0.8

Answer

A, C &D

Explanation

`omega=(1)/(sqrt(LC))=C=(1)/(sqrt(CL))impliesC=(1)/(omega^(2)L)`
`c=(1)/(400xx0.2)=12.5mF`
`I_(rms)=(e_(rms))/(R)=((10)/(sqrt(2)))/(5)=sqrt(2)A`
`P=i_(rms)^(2)R=2xx5=10W`
Quality factor `=(omegaL)/(R)=(20xx0.2)=0.8`