Question 228: AC fundamentals

Question

An ac circuit has an inductor and a resistor resistance R in series, such that X
L
= 3R. Now, a capacitor is added in series such that X
C
= 2R. The ratio of new power factor with the old power factor of the circuit is $$\sqrt 5 :x$$. The value of x is ___________.

Accepted Answer

$$\cos \phi  = {R \over {\sqrt {{R^2} + 3{R^2}} }}$$
$$ = {1 \over {\sqrt {10} }}$$
$$\cos \phi ' = {R \over {\sqrt {{R^2} + {R^2}} }}$$
$$ = {1 \over {\sqrt 2 }}$$
$${{\cos \phi '} \over {\cos \phi }} = {{\sqrt {10} } \over {\sqrt 2 }} = {{\sqrt 5 } \over 1}$$
$$	herefore$$ x = 1

AC fundamentals

An ac circuit has an inductor and a resistor resistance R in series, such that X L = 3R. Now, a capacitor is added in series such that X C = 2R. The ratio of new power factor with the old power factor of the circuit is $\sqrt 5 :x$. The value of x is ___________.

Integer / Numeric Answer Type