COMPONENTS IN AC CIRCUITS

• The resistor is not affecting by the fact the current is alternating.
• An inductor has a p.d. across it that changes with a changing current passsing through it, so will debhave differently in an AC circuit. Consider a circuit of pure inductance so V = L ^{d I} / _{d t}
  V = L ^d / _{d t} ( I₀ Sin( w t ))
  V = w L I₀ Cos( w t )
  so when t = 0, V₀ = w L I₀
  substituing V = V₀ Cos( w t ) Thus voltage is 90⁰ ahead of current. The reactance or resistance to current flow is given by ^V0 / I₀ is equal to Z_I = w L
• A capacitor only allows a current to flow through it when the voltage is changing., and the plates are charging. Consider a circuit with purely capacitance. Q = C V , or Q = C V₀ Sin( w t )
  Differenting with respect to time I = w C V₀ Cos( w t )
  ,
  so when t = 0, I₀ = w C V₀
  substituing I = I₀ Cos( w t ) Thus current is 90⁰ ahead of voltage. The reactance is equal to Z_C = ¹ / _{w C}

POWER DISSIPATED
Both Capacitors and Inductors only store energy, returning the same amount of energy they take up every cycle , hence their average power is 0. Resistors dissipate an averager power of V_rms I_rms or ¹/₂ I_max V_max

IMPEDANCE
Impedance is the combined effect of resistance, capacitance and inductance in a series circuit. By cosidering an AC circuit with a resitor, a capacitor and an inductor in, we can calculate the resultant relationship between voltage and current. The voltage in the inductor leads the voltage in the resistor by 90⁰, and the voltage in the capacitor lags by 90⁰. Drawing these on a phasor diagram, at their respectively different angles, it can be seen that