A series L R circuit connected with an ac source E = ( 25 sin 1000 t ) V has a power factor of 2 1 . If the source of emf is changed to E = ( 20 sin 2000 t ) V , the new power factor of the circuit will be :

For L R circuit, cos ϕ = ( X L ) 2 + R 2 R = 2 1 ⇒ R = X L Now, ω ′ = 2 ω Therefore, ( X L ) ′ = ω ′ L = 2 ω L = 2 X L Hence, cos ϕ ′ = ( 2 X L ) 2 + R 2 R = 5 1

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PhysicsEMI/ACQuality and Power factorMedium2 minQB

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A series $L R$ circuit connected with an ac source $E = (25 sin 1000 t) V$ has a power factor of $\frac{1}{2}$ . If the source of emf is changed to $E = (20 sin 2000 t) V$ , the new power factor of the circuit will be :

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Answer:

Solution:

For $L R$ circuit, $cos ϕ = \frac{R}{( X _{L} ) ^{2} + R ^{2}} = \frac{1}{2}$

$\Rightarrow R = X_{L}$

Now, $ω^{^{'}} = 2 ω$

Therefore, $(X_{L})^{^{'}} = ω^{^{'}} L = 2 ω L = 2 X_{L}$

Hence, $cos ϕ^{^{'}} = \frac{R}{( 2 X _{L} ) ^{2} + R ^{2}} = \frac{1}{5}$

Stream:JEESubject:PhysicsTopic:EMI/ACSubtopic:Quality and Power factor

⏱ 2mℹ️ Source: QB

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