Frequency Effects on L and C in DC Circuits

Electrical Circuit Analysis > Basic Elements of AC Circuit and Phasors

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For dc circuits, the frequency effect is zero, and the reactance of a coil is

$$X_L = 2\pi fL = 2\pi(0)L = 0 Ω$$

The use of the short-circuit equivalence for the inductor in dc circuits is now validated.

At very high frequencies, $X_L = 2\pi fL$ is very large, and for some practical applications the inductor can be replaced by an open circuit. In equation form,

$$\bbox[10px,border:1px solid grey]{X_L = 0 \,Ω} \, dc, \,f=0 \,Hz$$

and

$$\bbox[10px,border:1px solid grey]{X_L = \infty \,Ω} \, as, \,f \to \infty \,Hz$$

The capacitor can be replaced by an open-circuit equivalence in dc circuits since f = 0, and

$$ X_C = {1 \over 2\pi fC} = {1 \over 2\pi (0) C} \to \infty \, Ω$$

once again substantiating our previous action, At very high frequencies, for finite capacitances,

$$ X_C \downarrow= {1 \over 2\pi f \uparrow C} $$

is very small, and for some practical applications the capacitor can be replaced by a short circuit. In equation form

$$\bbox[10px,border:1px solid grey]{X_C = 0 \,Ω} \, \text{f=very high frequencies} $$

$$\bbox[10px,border:1px solid grey]{X_C \to \infty \,Ω} \, as f \to 0 $$

Table 1 reviews the preceding conclusions.

Table 1: Effect of high and low frequencies on the circuit model of an inductor and a capacitor.

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