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Two impedances Z1 = 8.66 + j5 and Z2 = 14.14 - j14.14 are connected in series. What is the power factor of this series combination?
- A0.7423
- B0.5
- C0.8547
- D0.9281
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CCommunity
Given that, Z1 = 8.66 + j5 and Z2 = 14.14 - j14.14
When they are connected in series, the equivalent impedance is
Zeq = Z1 + Z2 = 8.66 + j5 + 14.14 - j14.14 = 22.8 - j9.14 = R + jX
$(Z = \sqrt {{R^2} + {X^2}} = \sqrt {{{22.8}^2} + {{9.14}^2}} = 24.56\;{\rm{\Omega }})$
Power factor $(\cos \phi = \frac{R}{Z} = \frac{{22.8}}{{24.56}} = 0.928)$
When they are connected in series, the equivalent impedance is
Zeq = Z1 + Z2 = 8.66 + j5 + 14.14 - j14.14 = 22.8 - j9.14 = R + jX
$(Z = \sqrt {{R^2} + {X^2}} = \sqrt {{{22.8}^2} + {{9.14}^2}} = 24.56\;{\rm{\Omega }})$
Power factor $(\cos \phi = \frac{R}{Z} = \frac{{22.8}}{{24.56}} = 0.928)$