a)Derive the expression for the current flowing in an ideal capacitor and its reactance when connected to an ac source - Physics - Alternating Current

Question

a)Derive
the expression for the current flowing in an ideal capacitor and
its reactance when connected to an ac source of voltage V=Vosinwt
B) Draw its phasor diagram C)If resistance is added in series to
capacitor what changes will occur in current flowing in the circuit
and phase angle between voltage and current

Mousam Maity · Accepted Answer

Dear Student, Answer to question is given below: (a) We have: V = Vo sin ωt Also, V = qC {where, q = charge on capacitor }⇒Vo sin ωt = qC⇒ q = CVo sin ωtnow we know that, I = dqdt = ddt (CVo sin ωt) = ωCVo sin ωt∴ I = Vo1ωC sin (ωt + π2) Now, maximum current, Io = Vo1ωC × 1 { when sin (ωt + π2) = 1 ∴ I = Io sin (ωt + π2) Comparing with ohm's law, I = VR, with the above equation, we get, Io =Vo1ωC Hence, the capacitive reactance, Xc = 1ωC (b) Its phasor diagram is given below:

(c) If resistance is added in series to capacitor then,

Here, effective impedance, Z = R2 +Xc2As Z > R, current will be reduced In R-C circuit, voltage lags behind the current by a phase angle ϕ, where tan ϕ = VcVR= -IoXcIoR= -XcR { here negative sign is for lagging of alternating voltage behind alternating current } Regards,