A variable capacitor is connected to an ac source. what effect does decreasing the capacitance have on the reactance and current in this circuit?
Reactance Current
A) increases decreases
b) decreases no change
c) decreases increases
d) increases increases
e) no change no change
Xc= 1/2pi*f*C
current= constant/Xc= constant*f*C
Current remains constant. Answer is E.
To understand the effect of decreasing the capacitance on the reactance and current in this circuit, let's first understand the behavior of a variable capacitor in an AC circuit.
Variable capacitors are designed to change their capacitance by adjusting the distance between their plates. As the capacitance of a capacitor increases, it offers less opposition to the flow of current in the circuit. Conversely, as the capacitance decreases, it offers more opposition to the flow of current.
Now, let's consider the reactance of a capacitor in an AC circuit. Reactance is the opposition to the flow of AC current offered by a circuit component. It is calculated using the following formula: Xc = 1 / (2 * π * f * C), where Xc is the capacitive reactance, f is the frequency of the AC source, and C is the capacitance.
From the reactance formula, we can see that as the capacitance (C) decreases, the reactance (Xc) increases. This is because a smaller capacitance will lead to a larger value in the denominator of the formula, resulting in a higher capacitive reactance.
Now, let's consider the effect on the current. In an AC circuit, the current is inversely proportional to the reactance. In other words, as the reactance increases, the current decreases, and vice versa.
Based on this understanding, we can determine that decreasing the capacitance of the variable capacitor will result in an increase in reactance (option A), which in turn leads to a decrease in current (option A).
So, the correct answer to the question is:
A) increases the reactance and decreases the current.