Question

An RLC circuit has resistance R = 205 ⦠and inductive reactance XL = 369 â¦. Calculate the circuit's capacitive reactance XC (in â¦) if its power factor is cos(Ï) = 1.00 â 10^â2.

Answer 1

Explanation:

It is given that,

Resistance, R = 205 ohms

Inductive reactance, $X_L=369\ \Omega$

Power factor, $cos\phi=10^{-2}$

The power factor is given by :

$Cos\phi=\dfrac{R}{Z}$

R is the resistance of the circuit

Z is the impedance

We need to find the capacitive reactance of the circuit. Let it is $X_c$.

$cos\phi=\dfrac{R}{\sqrt{R^2+(X_L-X_c)^2}}$

$\dfrac{10^{-2}}{205}=\dfrac{1}{\sqrt{R^2+(X_L-X_c)^2}}$

$(X_L-X_c)^2=\dfrac{1}{2.37\times 10^{-9}}-R^2$

$(X_L-X_c)^2=\dfrac{1}{2.37\times 10^{-9}}-(205)^2$

$X_L-X_c=20540.17$

$X_c=20171.17\ \Omega$

Hence, this is the required solution.