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![**Why does a capacitor act as a short circuit at high frequencies?**
In electrical circuits, capacitors exhibit different behaviors depending on the frequency of the signal passing through them. At high frequencies, a capacitor acts as a short circuit. This phenomenon can be explained using the concept of capacitive reactance.
### Explanation:
- **Capacitive Reactance (Xc):** Capacitive reactance is the opposition that a capacitor offers to the change in voltage across it. It is inversely proportional to both the frequency (f) of the signal and the capacitance (C) of the capacitor, given by the formula:
\[
Xc = \frac{1}{2 \pi f C}
\]
- **High Frequency Behavior:** As the frequency (f) increases, the capacitive reactance (Xc) decreases. At very high frequencies, Xc approaches zero, implying that the capacitor presents minimal opposition to the flow of current, effectively acting like a short circuit.
### Application:
This behavior of capacitors is utilized in various applications where filtering of high-frequency signals is required, such as in bypass capacitors used in electronic circuits to eliminate noise.
Understanding the frequency-dependent behavior of capacitors is crucial in the design and analysis of AC circuits and various electronic applications.](https://content.bartleby.com/qna-images/question/adbb6fa3-6b43-4484-8eb2-c92bfed12f92/bdf82c09-00b7-47c1-a518-e3cbefdce202/8n0xi1_processed.png)
Transcribed Image Text:**Why does a capacitor act as a short circuit at high frequencies?**
In electrical circuits, capacitors exhibit different behaviors depending on the frequency of the signal passing through them. At high frequencies, a capacitor acts as a short circuit. This phenomenon can be explained using the concept of capacitive reactance.
### Explanation:
- **Capacitive Reactance (Xc):** Capacitive reactance is the opposition that a capacitor offers to the change in voltage across it. It is inversely proportional to both the frequency (f) of the signal and the capacitance (C) of the capacitor, given by the formula:
\[
Xc = \frac{1}{2 \pi f C}
\]
- **High Frequency Behavior:** As the frequency (f) increases, the capacitive reactance (Xc) decreases. At very high frequencies, Xc approaches zero, implying that the capacitor presents minimal opposition to the flow of current, effectively acting like a short circuit.
### Application:
This behavior of capacitors is utilized in various applications where filtering of high-frequency signals is required, such as in bypass capacitors used in electronic circuits to eliminate noise.
Understanding the frequency-dependent behavior of capacitors is crucial in the design and analysis of AC circuits and various electronic applications.
Expert Solution
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Introduction:
- A capacitor is a passive electrical component that is capable of storing energy in an electric field. It has two terminals and is also known as a condenser or condensator.
- A capacitor in an AC circuit has a property called reactance. This is the restriction on current flow due to the impedance of the capacitor. It depends on the frequency and is given by,
Here f is the frequency of the AC and C is the capacitance.
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