For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is α/10. The value of α i $s______.$
The circuit has R = 60 Ω, X(L) = 70 Ω and X(C) = 150 Ω.

Question

For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is α/10. The value of α i $s______.$

The circuit has R = 60 Ω, X(L) = 70 Ω and X(C) = 150 Ω.

G1 Physics · Accepted Answer

For a series LCR circuit, Z = √[R² + (X(L)-X(C))²]. Here, R = 60 Ω, X(L) = 70 Ω, X(C) = 150 Ω. Therefore, Z = √[60²+(70-150)²] = √(3600+6400) = 100 Ω. Power factor is cosφ = R/Z = 60/100 = 6/10. The question gives the power factor as α/10. Therefore, α = 6. Correct option: C.

For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is α/10. The value of α i s______. The circuit has R = 60 Ω, X(L) = 70 Ω and X(C) = 150 Ω.