what would happen to the impedance of a series circuit containing an inductor, capacitor and resistor if the supply frequency is varied from 0 to infinity Hz

At 0 Hz, the capacitor has high impedance

At high Hz, the inductor has high impedance

The circuit's impedance reaches a minimum at the resonant frequency of the LC portion.

The resistor keeps it from ever being zero, to protect the voltage source.

In a series circuit containing an inductor, capacitor, and resistor, the impedance is affected by the frequency of the power supply.

To understand what happens to the impedance as the frequency varies, we need to analyze the behavior of each component individually and then combine them.

1. Inductor:
The impedance of an inductor (ZL) is given by the formula ZL = jωL, where j is the imaginary unit, ω is the angular frequency (2πf, where f is the frequency in Hz), and L is the inductance in henries. Essentially, the impedance of an inductor increases with frequency, meaning that the inductor resists the flow of alternating current more as the frequency increases.

2. Capacitor:
The impedance of a capacitor (ZC) is given by the formula ZC = 1/(jωC), where C is the capacitance in farads. The impedance of a capacitor decreases with frequency, meaning that the capacitor allows more current to flow as the frequency increases.

3. Resistor:
The impedance of a resistor (ZR) is simply its resistance value (R). The impedance of a resistor is unaffected by frequency since it doesn't contain any reactive elements like inductors or capacitors.

Now, let's combine these components in a series circuit.

In a series circuit, the total impedance (Ztotal) is given by the formula:
Ztotal = ZR + ZL + ZC

As the supply frequency is varied from 0 to infinity Hz, the following happens:

- At very low frequencies (close to 0 Hz), the inductive reactance (jωL) dominates the total impedance, and Ztotal increases.
- As the frequency increases, the capacitive reactance (1/(jωC)) starts to become significant, offsetting the inductive reactance.
- At a certain frequency called the resonant frequency, the inductive and capacitive reactances cancel each other out (ZL = ZC), resulting in a purely resistive circuit where Ztotal is minimized.
- Above the resonant frequency, the capacitive reactance dominates, and Ztotal starts to decrease again.

In summary, in a series circuit containing an inductor, capacitor, and resistor, the impedance will vary with the supply frequency. It will generally increase at lower frequencies, reach a minimum at a resonant frequency, and then decrease at higher frequencies.