Place a resistor and capacitor in series with an AC source. What's the current?

If we had two resistors in series we'd add the individual resistances to find the equivalent resistance. We do the same thing here, only we add them as vectors, and we call the equivalent resistance the impedance of the circuit and give it the symbol Z.

Resistors want the voltage and current to be in phase, while capacitors want the voltage to lag behind the current by 90^o. When we add the resistances as vectors, then, the vectors are perpendicular.

Let's say we know the resistance R, capacitance C, and frequency f. To find the current follow these steps:

• Find the capacitive reactance of the capacitor:

  XC

  =

  1 wC

  , where w = 2pf

  
  
  
• Find the impedance of the circuit: Z² = [R² + X_C²]
  
  
• Find the current from V = IZ.
  
  
• Find the phase angle:

  tan(f)

  =

  –

  XC R

The phase angle is the angle between the voltage and current in the circuit. This is stated as the voltage relative to the current, so the phase angle is positive if the voltage is ahead of the current and negative if the voltage lags the current.