In series CR circuit excited by ac mains- C - 10 - F- R - 300- Find the power factor- Take - - 50 Hz Standard

The correct option is D 3√(19) Given: #160; C #160;=10^ 5F #160; #160; #160; #160; #160; #160; R =300Ω #160; #16 ...

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Standard XII

Physics

AC Applied to a Resistor

In series C...

Question

In series $CR$ circuit excited by ac mains, $C = 10 μ F, R = 300 Ω$ . Find the power factor.
Take $ν = 50$ Hz (Standard)

\frac{3}{\sqrt{17}}

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\frac{3}{\sqrt{16}}

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\frac{3}{\sqrt{18}}

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\frac{3}{\sqrt{19}}

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Solution

The correct option is D $\frac{3}{\sqrt{19}}$
Given: $C = 10^{- 5} F$ $R = 300 Ω$ $ν = 50$ Hz (Standard)

Capacitive reactance, $X_{c} = \frac{1}{w C} = \frac{1}{2 π (50) (10^{- 5})} = 318.5$ $Ω$

Power factor, $c o s ϕ = \frac{R}{\sqrt{R^{2} + X_{c}^{2}}}$

$∴$ $c o s ϕ = \frac{300}{\sqrt{(300)^{2} + (318.5)^{2}}} \approx \frac{3}{\sqrt{19}}$

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In series CR circuit excited by ac mains, C=10μF,R=300Ω. Find the power factor. Take ν=50 Hz (Standard)

The correct option is D 3√19Given: C=10−5F R=300Ω ν=50 Hz (Standard)Capacitive reactance, Xc=1wC=12π(50)(10−5)=318.5 ΩPower factor, cosϕ=R√R2+X2c∴ cosϕ=300√(300)2+(318.5)2≈3√19

In series $CR$ circuit excited by ac mains, $C = 10 μ F, R = 300 Ω$ . Find the power factor.
Take $ν = 50$ Hz (Standard)