CBSE Class 12 · 2005 · All India · Alternating CurrentShort Answer

WhatsApp Email

State the condition under which the phenomenon of resonance occurs in a series LCR circuit. Plot a graph showing the variation of current with the frequency of the a.c. source in a series LCR circuit.

Solution

Resonance in a series LCR circuit occurs when the inductive and capacitive reactances become equal:

X_{L} = X_{C} \Rightarrow ω L = \frac{1}{ω C} \Rightarrow f_{r} = \frac{1}{2 π L C}

At this frequency the net reactance is zero, the impedance is minimum (

Z = R

) and the current is maximum. The current-versus-frequency curve rises to a sharp peak at

f_{r}

and falls off on either side.

CBSE Class 12 Board · 2005 · All India · Subjective

Practise more: all CBSE board PYQs on Alternating Current →

More board questions on Alternating Current

An a.c. voltage is applied across an ideal inductor. The current in it
CBSE 2024View solution →
(a)(i) You are given three circuit elements X, Y and Z. They are connected one by one across a given a.c. source. It is found that V and I are in phase for element X, V leads I by $\frac{π}{2}$ for element Y, while I leads V by $\frac{π}{2}$ for element Z. Identify the elemen …
CBSE 2024View solution →
(b)(i) Describe the construction and working of a transformer and hence obtain the relation for $\frac{V _{s}}{V _{p}}$ in terms of the number of turns of the primary and secondary. (ii) Discuss four main causes of energy loss in a real transformer.
CBSE 2024View solution →
A series RC circuit with $R = 200 Ω$ and $C = (\frac{50}{π}) μ F$ is connected across an a.c. source of peak voltage $ε_{0} = 100$ V and frequency $ν = 50$ Hz. Calculate
(a) the impedance of the circuit ( $Z$ ),
(b) the phase angle ( $ϕ$ ), and
(c) the …
CBSE 2023View solution →
Laminated iron sheets are used to minimize ______ currents in the core of a transformer.
CBSE 2020View solution →
A resistance R and a capacitor C are connected in series to a source $V = V_{0} sin ω t$ . Find: (a) the peak value of the voltage across (i) the resistance and (ii) the capacitor; (b) the phase difference between the applied voltage and the current — which of them is ahead?
CBSE 2020View solution →