Question

The r.m.s. current in an ac circuit is 2 A. If the wattless current be $\sqrt { 3 } A$, what is the power factor

• A. $\frac { 1 } { \sqrt { 3 } }$
• B. $\frac { 1 } { \sqrt { 2 } }$
• C. $\frac { 1 } { 2 }$
• D. $\frac { 1 } { 3 }$

Answer 1

Answer: (C)

$\frac { 1 } { 2 }$

Answer 2

$\sqrt { 3 } = 2 \sin \phi$ ⇒ $\sin \phi = \frac { \sqrt { 3 } } { 2 }$

⇒ $\phi = 60 ^ { \circ }$ so p.f. $= \cos \phi = \cos 60 ^ { \circ } = \frac { 1 } { 2 }$ .