Fundamental Physics/Electricity/Electric circuits/RC Circuits

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RC Circuits[edit]

RC circuits are circuits that contain a resistor and a capacitor. These circuits are primarily used as frequency filters. There are two basic arrangements: high-pass and low-pass. A high-pass filter allows frequencies above the cut-off frequency to pass, while a low-pass filter allows frequencies beneath the cut-off frequency to pass. The arrangement of the resistor and the capacitor is what determines their behaviour.

Note that at a particular frequencly, called the cut-off frequency, the Capactive Reactance is equal to the Resistance value. (There is also an associated phase shift of 45 degrees.)

Substituting

we then have:

The cut-off frequency, defined as the frequency at which the signal power is attenuated by 50% (or 3.01 dB), is a function of the resistive and capacitive values. We can rearrange the above formula to solve for as follows:

RC series[edit]

A circuit of 2 component a resistor and a capacitor connected in series

Filter circuit[edit]

Low pass filter[edit]

When the capacitor is in parallel with the load while the resistor is in series with the capacitor and load, this creates a low pass filter.

Low pass filter.png

Low pass filter has a transfer function

Frequency response of Low pass filter

Cut off frequency, , frequency at which

High pass filter[edit]

When the resistor is in parallel with the load and the capacitor is in series with the resistor, a high pass filter is created.

High pass filter.png

High pass filter has a transfer function

Frequency response of High pass filter

Cut off frequency, , frequency at which

A single RC circuit creates a filter with a 20.0 dB/decade, or 6.02 dB/octave, slope.