# what is the value of power factor in the circuit at resonance

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## What is the power factor of LCR circuits at resonance?

What is the power factor of LCR circuits at resonance?. Ans: Hint : Power factor is the ratio of active power and apparent power. Reactive power of LCR combination is the difference between capacitive and inductive power. At resonance, capacitive an...

## What is the power factor of LCR circuits at resonance?

Last updated date: 13th Mar 2023

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**Hint :**Power factor is the ratio of active power and apparent power. Reactive power of LCR combination is the difference between capacitive and inductive power. At resonance, capacitive and inductive reactances are equal.

Formula Used: The formulae used in the solution are given here.

⇒P.F.= R Z ⇒P.F.=RZ where P.F. P.F.

is the power factor,

R R

is the reactance and

Z Z

is the total impedance.

⇒Z= R 2 +( X C − X L ) − − − − − − − − − − − − − √ ⇒Z=R2+(XC−XL) where , R R

is the reactance and

Z Z

is the total impedance and

X C XC

is the capacitive reactance and

X L XL

is the inductive reactance.

⇒ X C = 1 ωC ⇒XC=1ωC where C C

is the capacitance and

X L =ωL XL=ωL where L L is the inductance. ⇒ω=2πf ⇒ω=2πf where f f

is the frequency of AC source.

**Complete step by step answer**

Power factor is also the ratio of resistance of LCR circuit to its impedance. The power factor of an LCR circuit is the ratio of the resistance to the total impedance of the circuit. The total impedance consists of the magnitude of the phasor sum of the resistance, the capacitive reactance and the inductive reactance.

The power factor is a measure of the fraction of total power that is being used up or dissipated by a load resistor. Since, capacitors and inductors do not dissipate power but keep on exchanging them between the source and themselves, they do not utilize the power. The higher the power factor, the better it is for energy efficiency as a greater fraction of the power is available for utilization.

We know that, P.F.= R Z P.F.=RZ where P.F. P.F.

is the power factor,

R R

is the reactance and

Z Z

is the total impedance.

⇒Z= R 2 +( X C − X L ) − − − − − − − − − − − − − √ ⇒Z=R2+(XC−XL) where R R

is the reactance and

Z Z

is the total impedance and

X C XC

is the capacitive reactance and

X L XL

is the inductive reactance.

At resonance, X C = X L XC=XL . We know, X C = 1 ωC XC=1ωC where C C

is the capacitance and

X L =ωL XL=ωL where L L is the inductance. ⇒ω=2πf ⇒ω=2πf where f f

is the frequency of AC source.

⇒ 1 ωC =ωL ⇒1ωC=ωL ⇒ω= 1 LC − − − − √ ⇒ω=1LC Since, X C = X L XC=XL , thus X C − X L =0 XC−XL=0 . Total impedance Z Z is thus, Z= R 2 +0 − − − − − − √ Z=R2+0 ⇒Z=R. ⇒Z=R.

To find the power factor,

⇒P.F.= R Z =1 ⇒P.F.=RZ=1 . ∴ ∴

**The power factor at resonance is 1.**

**Note**

The voltage across the inductor and capacitor cancel each other. The total impedance of the circuit is only due to the resistor. The phase angle between voltage and current is zero.

⇒cosφ= R Z = R R =1. ⇒cosφ=RZ=RR=1.

The power factor is unity.

## The power factor of LCR circuit at resonance is

The power factor of LCR circuit at resonance is

Byju's Answer Standard XIII Physics Power Factor The power fac... Question

The power factor of LCR circuit at resonance is

A 0.707 B 1 C Zero D 0.5 Open in App Solution

The correct option is **B** 1

At resonance, LCR circuit behaves as purely resistive circuit, for purely resistive circuit power factor = 1.

Suggest Corrections 3

SIMILAR QUESTIONS

**Q.**The power factor of LCR circuit at resonance is

**Q.**For a series LCR circuit, power factor at resonance is equal to -

**Q.**In L-C circuit power factor at resonance is:

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**Q.**In L-C-R circuit power factor at resonance is

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## [Solved] The power factor in a series LCR circuit at resonance is:

Concept: Resonance: In series LCR circuits, Resonance is a condition in which the inductive reactance and capacitive reactance are equal and lie opposite in

Home Physics Electromagnetic Oscillations and Alternating Current Alternating Current

## Question

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## The power factor in a series LCR circuit at resonance is:

1 1 / √2 zero infinite

## Answer (Detailed Solution Below)

Option 1 : 1

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## Detailed Solution

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**Concept:**

**Resonance:**In series LCR circuits, Resonance is a condition in which the

**inductive reactance**and

**capacitive reactance**are

**equal and lie opposite in phase**, so

**cancel out each other**. Only,

**resistance is left as impedance.**

Formula for power factor is calculated as ratio of resistance to total impedance.

ϕ=resistanceofcircuitTotalimpedance

Fig: a Series RLC circuit

Figure Phasor diagram for series RLC circuit

**Explanation:**

The **power factor** of a **series LCR circuit** at **resonance **will be **1** due to the presence of only **resistance as an effective impedance**.

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