If the frequency of an AC source is doubled, the impedance of a pure resistor ____________.
remains unchanged
To determine the effect of changing the frequency of an AC source on the impedance of a pure resistor, we need to understand some basic electrical concepts:
- Impedance of a Resistor: In an AC circuit, the impedance \(Z\) of a pure resistor is given by its resistance \(R\). This is because a resistor does not have any reactive components (inductance or capacitance) that would cause its impedance to depend on frequency. Therefore, impedance \(Z\) of a pure resistor is simply \(Z = R\).
- Effect of Frequency: The impedance of a resistor is independent of the frequency of the AC supply. This means that changing the frequency of the AC source will not affect the impedance of a pure resistor. The impedance remains constant regardless of frequency changes.
Based on these principles, when the frequency of an AC source is doubled, the impedance of a pure resistor remains unchanged.
Therefore, the correct answer is: remains unchanged.
Let's evaluate the options:
- Remains unchanged: Correct - As explained, because resistive impedance is independent of frequency.
- Quadruples: Incorrect - Impedance of a pure resistor is not influenced by frequency, so it does not quadruple.
- Doubles: Incorrect - Similar reasoning to quadruples; impedance remains the same.
- Halves: Incorrect - The impedance cannot halve as the frequency increases; it remains unchanged.
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