a variable frequency a.c. source is connected to a capacitor. will the displacement current increases or decrease with decrease in frequency?

To understand how the displacement current behaves when the frequency of an alternating current (AC) source connected to a capacitor changes, we need to delve into the concept of displacement current and its relationship with frequency and capacitance.

What is Displacement Current?

Displacement current is a term introduced by James Clerk Maxwell to describe a phenomenon that occurs in capacitors when they are subjected to a changing electric field. It is not a current in the traditional sense, as it does not involve the flow of charge carriers like electrons. Instead, it represents the changing electric field between the plates of a capacitor, which can produce effects similar to those of a conventional current.

The Role of Frequency

In an AC circuit, the frequency of the source affects how quickly the voltage across the capacitor changes. The relationship between the displacement current (I_d), the capacitance (C), and the rate of change of voltage (dV/dt) can be expressed mathematically as:

I_d = C * (dV/dt)

Here, dV/dt represents the rate of change of voltage across the capacitor. In an AC circuit, this voltage varies sinusoidally, and its rate of change is directly related to the frequency of the AC source.

Impact of Decreasing Frequency

When the frequency of the AC source decreases, the rate of change of voltage (dV/dt) also decreases. This is because a lower frequency means that the voltage waveform takes longer to complete one full cycle, resulting in a slower change in voltage over time. Consequently, since the displacement current is directly proportional to this rate of change, a decrease in frequency leads to a decrease in the displacement current.

Example for Clarity

• Consider a capacitor with a capacitance of 1 microfarad (μF) connected to a 60 Hz AC source. The voltage across the capacitor changes relatively quickly, resulting in a significant displacement current.
• If we switch to a 10 Hz AC source, the voltage changes much more slowly, leading to a reduced displacement current.

Summarizing the Effects

In summary, as the frequency of the AC source decreases, the displacement current flowing through the capacitor also decreases. This relationship highlights the importance of frequency in AC circuits and its impact on the behavior of capacitors.

Understanding these concepts not only helps in grasping the behavior of capacitors in AC circuits but also lays the groundwork for more advanced topics in electromagnetism and circuit theory.