How is the impedance of an RC circuit affected when an inductor is added in series?

The impedance of an RC circuit is given by:

Z_RC = √(R² + (1 / ωC)²)

Where:

R is the resistance of the resistor in ohms (Ω).

C is the capacitance of the capacitor in farads (F).

ω (omega) is the angular frequency of the AC signal in radians per second, given by ω = 2πf, where f is the frequency in hertz (Hz).

Now, when an inductor is added in series to the RC circuit, the impedance changes to a series RLRC circuit, and the impedance, in this case, is given by:

Z_RLRC = √(R² + (ωL - 1 / ωC)²)

Where:

L is the inductance of the inductor in henrys (H).

In the RC circuit, the impedance is dominated by the capacitor's reactance, which decreases with increasing frequency. As the frequency goes to zero (DC), the impedance approaches the resistance (Z → R). On the other hand, at high frequencies, the capacitor's impedance becomes very low, making the overall impedance of the RC circuit smaller.

When you add an inductor to the circuit, its impedance is given by ωL, and it increases linearly with frequency. So, as the frequency increases, the inductor's impedance becomes more significant in the overall impedance of the circuit.

The overall effect is that the impedance of the RLRC circuit will vary with frequency, with the capacitor's impedance dominating at low frequencies and the inductor's impedance becoming significant at high frequencies. The resistor's impedance remains constant as it is frequency-independent.

In summary, adding an inductor in series with an RC circuit results in a more complex impedance response, and the circuit's behavior becomes frequency-dependent due to the combined effects of the resistor, capacitor, and inductor.