Question

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)/(po) (mu)F`, 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) ` gtP_(C )lt`.
`(m) i(t)`, `V_(R )(t),and V_(C)(t)`.

Answer 1

`X_(C)=10^(6)/(100/pi(2pi50))=100 Omega`
(i)`Z=sqrt(R^(2)+Xc^(2))=sqrt(100^(2)+(100)^(2))=100sqrt2Omega`
(ii)`tan phi=(Xc)/R=1 therefore phi=45^(@)`
(iii)Power factor =`cos theta=1/sqrt2` ltbtgt (iv)Current `I_(rma)=V_(rma)/Z=200/(100sqrt2)=sqrt2A`
(v)Maximum current =`I_(rmasqrt2=2A`
(vi)voltage across `R=V_(Rms)=I_(rms)R=sqrt2xx100` volt
(vii)voltage across `C=V_(Cms)=I_(rms)X_(C)=sqrt2xx100` volt
(viii)max voltage across `R=sqrt2 V_(Rms)=200` volt
(ix)max voltage across `C=sqrt2 V_(C.rms)=200` volt
(x)`ltPgt =V_(rms)I_(rms)cosphi=200xxsqrt2xx1/sqrt2=200` volt
(xi)`ltP_(R)gt=I_(rms)^(2)R=200 W`
(xii)`ltP_(C)gt=0`