A series LCR circuit is tuned to resonance. The impedance of the circuit at resonance is :

Question

A series LCR circuit is tuned to resonance. The impedance of the circuit at resonance is : (A) [R2+(ω L-(1/ω C))2]1 / 2 (B) [R2+(ω L)2+((1/ω C))2]1 / 2 (C) [R2+((1/ω C))2]1 / 2 (D) R

Tardigrade Admin · Accepted Answer

In a series L-C-R circuit, the impedance

Z

is given by

Z = R^{2} + (ω L - \frac{1}{ω C})^{2}

At resonance Inductive reactance

=

capacitance reactance

∴ X_{L} = X_{C}

\Rightarrow ω L = \frac{1}{ω C}

and

tan ϕ = 0

,
i.e.,

ϕ = 0

, the emf and current are in phase.

∴ Z = R^{2} + 0 = R

which is the minimum value

Z

can have.

Q. A series LCR circuit is tuned to resonance. The impedance of the circuit at resonance is :

$[R^{2} + (ω L - \frac{1}{ω C})^{2}]^{1/2}$

$[R^{2} + (ω L)^{2} + (\frac{1}{ω C})^{2}]^{1/2}$

$[R^{2} + (\frac{1}{ω C})^{2}]^{1/2}$

$R$

Q. A series LCR circuit is tuned to resonance. The impedance of the circuit at resonance is :

[R2+(ωL−ωC1​)2]1/2

[R2+(ωL)2+(ωC1​)2]1/2

[R2+(ωC1​)2]1/2

R

In a series L-C-R circuit, the impedance Z is given by Z=R2+(ωL−ωC1​)2​ At resonance Inductive reactance = capacitance reactance ∴XL​=XC​ ⇒ωL=ωC1​ and tanϕ=0, i.e., ϕ=0, the emf and current are in phase. ∴Z=R2+0​=R which is the minimum value Z can have.

$[R^{2} + (ω L - \frac{1}{ω C})^{2}]^{1/2}$

$[R^{2} + (ω L)^{2} + (\frac{1}{ω C})^{2}]^{1/2}$

$[R^{2} + (\frac{1}{ω C})^{2}]^{1/2}$

$R$