How does the impedance of an RC circuit vary with frequency?

The impedance of an RC circuit is given by the formula:

Z = R + 1 / (jฯC)

where:

Z is the impedance (complex quantity),

R is the resistance in ohms,

j is the imaginary unit (โ(-1)),

ฯ is the angular frequency of the AC signal in radians per second, and

C is the capacitance in farads.

The term 1 / (jฯC) represents the reactance due to the capacitor, and its value changes with the frequency of the AC signal. Let's examine how the impedance varies with frequency:

At low frequencies (ฯ โ 0):

The reactance term, 1 / (jฯC), becomes very large.

As a result, the impedance is dominated by the capacitor's reactance, and the resistance has little effect.

The impedance approaches infinity (Z โ โ), acting as an open circuit.

The current flow through the circuit is minimal.

At high frequencies (ฯ โ โ):

The reactance term, 1 / (jฯC), becomes very small.

The impedance is dominated by the resistance, and the capacitor's reactance has little effect.

The impedance approaches the resistance value (Z โ R), acting as a purely resistive circuit.

The current flow through the circuit is limited by the resistance.

At a specific frequency (ฯ = 1 / RC):

The reactance term, 1 / (jฯC), becomes equal to the resistance R.

The impedance becomes purely real (no imaginary part) and reaches its minimum value.

This frequency is known as the corner frequency or cutoff frequency (f_c = 1 / 2ฯRC).

At this frequency, the capacitor's reactance cancels out the resistance, and the impedance is equal to R.

Overall, the impedance of an RC circuit varies with frequency, showing different characteristics at low, high, and specific frequencies. This frequency-dependent behavior is a fundamental aspect of AC circuits involving reactive components like capacitors and inductors.