An inductor is connected to an AC voltage source. Increasing the frequency of the source _ the rms current through the inductor. a. decreases b. does not change c. increases
The Correct Answer and Explanation is:
Correct Answer: a. decreases
Explanation:
An inductor in an alternating current (AC) circuit resists changes in current due to its property called inductive reactance. The inductive reactance XLX_LXL is given by the formula: XL=2πfLX_L = 2\pi f LXL=2πfL
Where:
- XLX_LXL is the inductive reactance (in ohms),
- fff is the frequency of the AC source (in hertz),
- LLL is the inductance of the inductor (in henries),
- π\piπ is approximately 3.1416.
As seen in this equation, the inductive reactance increases directly with the frequency. When the frequency of the AC voltage source is increased, the value of XLX_LXL also increases.
The current in an AC circuit that contains only an inductor is given by: Irms=VrmsXLI_{\text{rms}} = \frac{V_{\text{rms}}}{X_L}Irms=XLVrms
Where:
- IrmsI_{\text{rms}}Irms is the root mean square current,
- VrmsV_{\text{rms}}Vrms is the root mean square voltage,
- XLX_LXL is the inductive reactance.
As XLX_LXL increases with frequency, and assuming the voltage VrmsV_{\text{rms}}Vrms remains constant, the denominator of the equation becomes larger. As a result, the current IrmsI_{\text{rms}}Irms becomes smaller.
Therefore, increasing the frequency of the source causes the inductor to oppose the current more strongly. This leads to a decrease in the rms current flowing through the inductor.
This behavior is a fundamental property of inductors in AC circuits and is important in the design of filters, transformers, and other electronic components. It also explains why inductors are used to block high-frequency signals while allowing low-frequency ones to pass.
