An ac source is connected to a capacitor C. Due to decrease in its operating frequency:
capacitive reactance remains constant
capacitive reactance decreases
displacement current increases
displacement current decreases
The Correct Option is D
Approach Solution - 1
The correct option is (D): displacement current decreases When an AC source is connected to a capacitor, the capacitive reactance (Xc) is given by:
\(X_c=\frac{1}{(2\times\pi\times f \times C)}\)
where: f is the frequency of the AC source C is the capacitance of the capacitor
As we can see from the above equation, the capacitive reactance is inversely proportional to the frequency of the AC source.
So, if the frequency of the AC source decreases, the capacitive reactance will increase.
Therefore, the statement "capacitive reactance remains constant" is not correct.
The statement "capacitive reactance decreases" is also not correct.
The statement "displacement current increases" is also not correct because the displacement current in a capacitor is directly proportional to the rate of change of the electric field, which is not affected by the frequency of the AC source.
Therefore, the correct answer is: "displacement current decreases". The displacement current in a capacitor is given by:
\(I_d=C\times\frac{dV}{dt}\)
where: Id is the displacement current C is the capacitance of the capacitor \(\frac{dV}{dt}\) is the rate of change of the voltage across the capacitor
As the frequency of the AC source decreases, the rate of change of voltage across the capacitor decreases, which in turn decreases the displacement current.
Approach Solution -2
When an AC source is connected to a capacitor C, the capacitor offers a capacitive reactance (Xc) to the circuit, which is given by:
\(X_c=\frac{1}{2\pi f_C}\)
where f is the frequency of the AC source and C is the capacitance of the capacitor.
Now, when the operating frequency of the AC source is decreased, the capacitive reactance of the capacitor increases, because the capacitive reactance is inversely proportional to the frequency of the source. This means that option 2 is incorrect, and option 1 is also incorrect.
When a capacitor is connected to an AC source, it charges and discharges repeatedly as the polarity of the voltage across it changes with time. This charging and discharging of the capacitor results in a displacement current, which is a flow of electric charge that does not involve the motion of charge carriers (i.e. electrons) through a conductor.
As the frequency of the AC source decreases, the time available for the capacitor to charge and discharge also increases, resulting in an increase in the magnitude of the displacement current. Therefore, option 3 is incorrect, and option 4 is correct.
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Concepts Used:
Alternating Current
An alternating current can be defined as a current that changes its magnitude and polarity at regular intervals of time. It can also be defined as an electrical current that repeatedly changes or reverses its direction opposite to that of Direct Current or DC which always flows in a single direction as shown below.
Alternating Current Production
Alternating current can be produced or generated by using devices that are known as alternators. However, alternating current can also be produced by different methods where many circuits are used. One of the most common or simple ways of generating AC is by using a basic single coil AC generator which consists of two-pole magnets and a single loop of wire having a rectangular shape.
Application of Alternating Current
AC is the form of current that are mostly used in different appliances. Some of the examples of alternating current include audio signal, radio signal, etc. An alternating current has a wide advantage over DC as AC is able to transmit power over large distances without great loss of energy.