CBSE Class 12 · 2011 · All India · Alternating CurrentShort Answer

An alternating voltage of frequency

f

is applied across a series LCR circuit. Let

f_{r}

be the resonance frequency of the circuit. Will the current in the circuit lag, lead, or remain in phase with the applied voltage when
(i)

f > f_{r}

, and
(ii)

f < f_{r}

? Explain your answer in each case.

Answer: (i) $f > f_{r}$ : current lags the voltage (inductive).
(ii) $f < f_{r}$ : current leads the voltage (capacitive).

Solution

The reactances are

X_{L} = 2 π f L

(rising with

f

) and

X_{C} = \frac{1}{2 π f C}

(falling with

f

); at resonance

X_{L} = X_{C}

.
(i) For

f > f_{r}

X_{L} > X_{C}

, so the circuit is net inductive and the current lags the applied voltage.
(ii) For

f < f_{r}

X_{C} > X_{L}

, so the circuit is net capacitive and the current leads the applied voltage.

CBSE Class 12 Board · 2011 · All India · Subjective