# RC Low-Pass Filters

The resistor-capacitor (RC) low-pass filter circuit diagram is given below. The voltage across the resistor is given by Ohm's law and is VR = I x R. The voltage across the capacitor, Vout lags the current by 900 and is given by Vout = I x XC, where XC is the capacitive reactance.

Looking at the diagram, Pythagoras's Theorem can be used to obtain the expression Vin = (VR2 + Vout2) ^ 0.5.

The impedance (ie combination of resistance and reactance) looking from the supply into the circuit is given by Z = (R2 + XC2) ^ 0.5.

The current in the circuit, I, is equal to Vin / Z.

MathML formulaFormula ImageStraight text formula
$f c = 1 2πRC$ fc = 1 / 2πRC

Where

fc = cut off frequency, Hertz

= that frequency at which output power has fallen by half

= that frequency at which output voltage has fallen by 1/(2^0.5) = 0.707

R = resistance in Ohms