A series L R circuit connected with an ac source E = ( 25 sin 1000 t ) V has a power factor of 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 :

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

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PhysicsEMI/ACQuality and Power factorMedium2 minPYQ_2024

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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 $\frac{1}{\sqrt{2}}$ . If the source of emf is changed to $E = (20 \sin 2000 t) V$ , the new power factor of the circuit will be :

Options:

Answer:

Solution:

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

$\Rightarrow R = X_{L}$

Now, $ω^{'} = 2 ω$

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

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

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

⏱ 2mℹ️ Source: PYQ_2024

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