Name: Alternating Current
Uploaded: 2019-07-19
Duration: 4 min 17 s
Description: An alternating current is an electric current which periodically reverses direction and changes its magnitude continuously with time. Learn more.

Question

Define inductive reactance and capacitive reactance, write their units and plot a graph for

X_{L}

and

X_{C}

with frequency of an alternating current.

Accepted Answer

Inductive Reactance : The peak value of current in the coil is

$I_{0} = \frac{V_{0}}{ωL}$

Applying Ohm’s law, we find that the product $ωL$ has the dimensions of resistance. It represents the ‘effective opposition’ of the coil to the flow of alternating current. It is known as the ‘reactance of the coil’ or ‘inductive reactance’ and is denoted by $X_{L}$ . Thus

$X_{L} = ωL = 2 πfL$

Where $f$ is the frequency of the alternating current. Thus, the inductive reactance increases with increasing frequency of the current $(X_{L} \propto f)$ . The graph between $X_{L}$ and f is, therefore, a straight line

The increase in inductive reactance with increase in frequency is easy to understand. At a higher frequency of current, the flux through the coil will change at a higher rate which will result in a higher back voltage in the coil and hence greater opposition for the flow of current. This means higher inductive reactance. When L is in henry and /in hertz (cycle/second), then $X_{L} (= 2 πfL)$ is in ohm. The inductive reactance $X_{L} (= 2 πfL)$ is zero for d.c. for which $f = 0$ .

Capacitive Reactance : The peak value of current in the capacitor circuit is

$I_{0} = \frac{V_{0}}{1 / ωC}$

Applying Ohm’s law, we find that the quantity $1 / ωC$ has the dimensions of resistance. It represents the ‘effective opposition’ of the capacitor to the flow of alternating current. It is known as the ‘reactance of the capacitor’ or ‘capacitive reactance’ and is denoted by $X_{C}$ . Thus

$X_{C} = \frac{1}{ωC} = \frac{1}{2 πfC}$

Thus, the capacitive reactance decreases with increasing frequency of current $(X_{C} \propto 1 / f)$ . The graph between Xc and / is, therefore, a rectangular hyperbola .
The decrease in capacitive reactance with increase in frequency is easy to understand. At a higher frequency, the charge on the capacitor plates will vary more rapidly (dq/dt will be higher), resulting in an increase in the instantaneous current (/ = dq/dt). This means lower capacitive reactance.

When C is in farad and f is in hertz then $X_{C}$ is in ohm.
The capacitive reactance $X_{C} (= 1 / 2 πfC)$ is infinite for DC for which $f = 0$ .
The reciprocal of reactance (inductive or capacitive) is called ‘susceptance’ of the AC circuit. It is measured in ‘mho’ or $^{'} {ohm}^{- 1}, (Ω^{- 1})$ or ‘siemen’ (S).

Define inductive reactance and capacitive reactance, write their units and plot a graph for $X_{L}$ and $X_{C}$ with frequency of an alternating current.

Important Questions on Alternating Current

Learn and Prepare for any exam you want !

Define inductive reactance and capacitive reactance, write their units and plot a graph for XL and XC with frequency of an alternating current.

Important Questions on Alternating Current

Learn and Prepare for any exam you want !

Define inductive reactance and capacitive reactance, write their units and plot a graph for $X_{L}$ and $X_{C}$ with frequency of an alternating current.