Question

An inductor, a resistor and a capacitor are joined in series with AC source. As the frequency of the source is slightly increased from a very low value, the reactance:
A) The inductor increases.
B) The resistor increases.
C) The capacitor increases.
D) The circuit increases.

Answer 1

Reactance is the resistance offered by the elements inductor or capacitance. The formula of reactance of the capacitor can be used to solve this problem. Also the reactance of the inductor can help to solve this problem as the circuit involves the inductor and capacitor in series with an AC source.

Formula used: The formula used to calculate the resistance for a inductor is given by
${X_L} = 2\pi fL$ Where $L$ is the inductance of the inductor and $f$ is the frequency. Also the formula of the reactance of the capacitor is given by ${X_c} = \dfrac{1}{{2\pi fC}}$ where $f$ is the frequency and $C$ is the capacitance of the capacitor.

Complete step by step answer:
As it is given that the circuit has a capacitor and the formula of reactance is given by ${X_c} = \dfrac{1}{{2\pi fC}}$ here the reactance is inversely proportional to the capacitance which means that the reactance will decrease if the frequency is increased.
The circuit has an inductor, a capacitance and a resistor with an AC source. So the reactance due to the inductor is given by ${X_L} = 2\pi fL$ here the reactance is proportional to the frequency of the wave and therefore the reactance of the inductor increases.

Note: Students should observe that if we need to calculate the total resistance then we simply put the formula for series and solve therefore as the reactance of the inductor increases with increases in frequency at the same time the reactance due to the capacitance decrease, so one of the term is increasing but another term is decreasing which will not put much increasing effect on the circuit as they are in series therefore we have selected the correct option as the increase of the reactance of the inductor and not of the circuit.