A series LCR circuit is connected to an AC source of 220 V , 50 Hz . The circuit contains a resistance R = 80Ω , an inductor of inductive reactance X L = 70Ω , and a capacitor of capacitive reactanc

Question

A series LCR circuit is connected to an AC source of 220 V , 50 Hz . The circuit contains a resistance R = 80Ω , an inductor of inductive reactance X L ​ = 70Ω , and a capacitor of capacitive reactance X C ​ = 130Ω . The power factor of circuit is 10 x ​ . The value of x is:

TestHub · Accepted Answer

Power factor in LCR circuit is given by,

$cos ϕ = \frac{R}{Z}$ , where, $Z$ is the total impedance of the circuit.

So, $cos ϕ = \frac{R}{R ^{2} + ( X _{C} - X _{L} ) ^{2}}$ Putting the values, we have

$\Rightarrow cos ϕ = \frac{80}{( 80 ) ^{2} + ( 60 ) ^{2}}$

$\Rightarrow cos ϕ = \frac{80}{100} \Rightarrow \frac{8}{10}$

Thus, the value of $x = 8$ .

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