For the series LCR circuit connected with 220 V, 50 Hz a.c. source as shown in the figure, the power factor is $\frac{α}{10}$ . The value of $α$ is ________. [2026]

Question

Smart Achievers · Accepted Answer

(4)

$Power factor = \frac{R}{Z}$

$Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}$

$= \sqrt{60^{2} + {(150 - 70)}^{2}} = 100 Ω$

$∴$ $Power factor = \frac{60}{100} = \frac{6}{10}$

$Then a = 6$

Solution

Q.
For the series LCR circuit connected with 220 V, 50 Hz a.c. source as shown in the figure, the power factor is $\frac{α}{10}$ . The value of $α$ is ________. [2026]

1 10

2 4

3 8

4 6

Ans.
(4)

$Power factor = \frac{R}{Z}$

$Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}$

$= \sqrt{60^{2} + {(150 - 70)}^{2}} = 100 Ω$

$∴$ $Power factor = \frac{60}{100} = \frac{6}{10}$

$Then a = 6$

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Solution

Q. For the series LCR circuit connected with 220 V, 50 Hz a.c. source as shown in the figure, the power factor is α10. The value of α is ________. [2026]

1 10

2 4

3 8

4 6

Ans. (4) Power factor=RZ Z=R2+(XL-XC)2 =602+(150-70)2=100 Ω ∴ Power factor=60100=610 Then a=6

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Q.
For the series LCR circuit connected with 220 V, 50 Hz a.c. source as shown in the figure, the power factor is $\frac{α}{10}$ . The value of $α$ is ________. [2026]

Ans.
(4)

$Power factor = \frac{R}{Z}$

$Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}$

$= \sqrt{60^{2} + {(150 - 70)}^{2}} = 100 Ω$

$∴$ $Power factor = \frac{60}{100} = \frac{6}{10}$

$Then a = 6$