Answer the following questions:
An applied voltage signal consists of a superposition of a dc voltage and an a.c. voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across C and the ac signal across L.

Solution

For high frequency, the inductive reactance for a.c. is X_L = ωL = ∞ and, capacitance of reactance

X_{C} = \frac{1}{ωC} = 0 .

Hence, capacitor does not offer any resistance for A.C. Thus a.c. signal appears across L only.

Consequently, X_L for d.c., X_L = ωL = 0 and

X_{C} = \frac{1}{ωC} = \infty

Therefore, d.c. signal appears across C only.

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