Consider two series resonant circuits with components L1C1 and L2C2 with same resonant frequency - -When connected in series- the resonant frequency of the combination is

A series LCR circuit is tuned to resonance. If the angular frequency of the applied AC voltage at resonance is $ω$ , the impedance of the circuit then is:

Q. An LCR series circuit contains

L = 8 H

, C

=

0.5

μ

F and R

=

100

Ω

.The resonant frequency of the circuit is

Q. A circuit containing resistance

R_{1}

, Inductance

L_{1}

and capacitance

C_{1}

connected in series resonates at the same frequency

n

as a second combination of

R_{2}

L_{2}

and

C_{2}

. If the two are connected in series, then the circuit will resonate at:

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Consider two series resonant circuits with components L1C1 and L2C2 with same resonant frequency , ω.When connected in series, the resonant frequency of the combination is

The correct option is C ωInitially, ω=1√L1C1 and ω=1√L2C2Finally, Leq=L1+L2 Ceq=C1C2C1+C2 ω′=1√LeqCeqfrom above equation, we will get ω′=ω

Consider two series resonant circuits with components $L_{1} C_{1}$ and $L_{2} C_{2}$ with same resonant frequency , $ω$ .When connected in series, the resonant frequency of the combination is

The correct option is C $ω$
Initially, $ω = \frac{1}{\sqrt{L_{1} C_{1}}}$ and

$ω = \frac{1}{\sqrt{L_{2} C_{2}}}$

Finally, $L_{e q} = L_{1} + L_{2}$

$C_{e q} = \frac{C_{1} C_{2}}{C_{1} + C_{2}}$

$ω^{'} = \frac{1}{\sqrt{L_{e q} C_{e q}}}$

from above equation, we will get $ω^{'} = ω$