Understanding Inductor Impedance and Frequency

The question asks how the impedance of an inductor changes as the frequency increases. Let's explore the concept of inductor impedance.

In AC circuits, components like resistors, capacitors, and inductors oppose the flow of alternating current. This opposition is called impedance ($Z$). For a pure inductor, the opposition to AC current is specifically called inductive reactance ($X_L$).

The inductive reactance ($X_L$) of an inductor is given by the formula:

$$X_L = 2\pi fL$$

Where:

• \(X_L\) is the inductive reactance, measured in ohms (\(\Omega\)).
• \(f\) is the frequency of the AC current, measured in hertz (Hz).
• \(L\) is the inductance of the inductor, measured in henries (H).
• \(\pi\) is a mathematical constant, approximately 3.14159.

For a pure inductor, the impedance ($Z$) is equal to its inductive reactance ($X_L$). So, $Z = X_L$.

Looking at the formula \(X_L = 2\pi fL\), we can see how inductive reactance relates to frequency (\(f\)) and inductance (\(L\)). The term \(2\pi L\) is a constant for a given inductor. Therefore, the inductive reactance \(X_L\) is directly proportional to the frequency \(f\).

$$X_L \propto f$$

This means that if the frequency \(f\) increases, the inductive reactance \(X_L\) also increases. Since the impedance of a pure inductor is equal to its inductive reactance ($Z = X_L$), an increase in frequency leads to an increase in the impedance of the inductor.

Let's consider the options based on this understanding:

• decreases: This would imply an inverse relationship between frequency and impedance, which is incorrect for an inductor.
• remains same: This would imply impedance is independent of frequency, which is incorrect for an inductor.
• increases: This aligns with our analysis that inductive reactance and thus impedance are directly proportional to frequency.
• is zero: Impedance is zero only in specific theoretical conditions (like at DC frequency, f=0) and not a general behavior as frequency increases from a non-zero value.

Therefore, as the frequency increases, the impedance of the inductor increases.

Revision Table: Inductor Impedance vs Frequency

Additional Information: Impedance of Other Components

Impedance is a general concept for AC circuits. Different components behave differently with frequency:

• Resistor (R): The impedance of a pure resistor is simply its resistance \(R\). Resistance is generally considered independent of frequency. So, the impedance of a resistor remains essentially constant as frequency changes. \(Z_R = R\).
• Capacitor (C): The opposition to AC current offered by a capacitor is called capacitive reactance ($X_C$). The formula for capacitive reactance is:

  $$X_C = \frac{1}{2\pi fC}$$

  Where \(C\) is the capacitance. For a capacitor, the capacitive reactance \(X_C\) is inversely proportional to the frequency \(f\).

  $$X_C \propto \frac{1}{f}$$

  This means as frequency increases, the impedance of a capacitor decreases. \(Z_C = X_C\).

In summary, inductors and capacitors have impedance that varies with frequency, while resistors typically do not.