In an RC series circuit(in fig), the rms voltage of source is 200V and its frequency is 50 Hz, if `R=100 Omega and C=(100)/(pi) muF`, find
(a) inpedance of the circuit.
(b) power factor angle,
(c ) power factor,
(d) current,
(e) maximum current
(f) voltage across R,
(g) voltage across C,
(h) maximum voltage across R,
(i) maximum voltage across C,
(j) `ltPgt`,
(k) ` ltP_(R )gt`.
(l) ` ltP_(C )gt`
(m) `i(t)`, `V_(R )(t),and V_(C)(t)`.

Explanation

`X_(C)=(10^(6))/((100)/(pi)(2pi50))=100Omega`
(i) `Z=sqrt(R^(2)+X_(c^(2))=sqrt(100^(2)+(100)^(2)=100sqrt2Omega`
(ii) `tan phi =(X_(c))/(R )=1 therefore phi-=45^(@)`
(iii) `"Power factor"=cos phi=(1)/(sqrt2)`
`(iv)"Current" I_("rms")=(V_(rms"))/(Z)=(200)/(100sqrt2)=sqrt2A`
`(v)"Maximum current"=I_("rms")sqrt2=2A`
`(vi)"voltage across"R=V_(R,"rms")=I_("rms")R=sqrt2xx100"volt"`
`(viii)"max voltage across R "=sqrt2 V_(R,"rms")X_(C)=sqrt2xx100"volt"`
`(ix)"max voltage acorss C"=sqrt2V_(C,"rms")=200"volt"`
`(x) lt P gt =V_("rms")I_("rms")cos phi=200xxsqrt2xx (1)/(sqrt2)=200"volt"`
`("xi") lt P_(R)=I_("rms")cos phi=200W`
`("xii") lt P_(C) =0`