Question 284: AC fundamentals

Question

A series LCR circuit is connected to an a.c. source of $230 \mathrm{~V}, 50 \mathrm{~Hz}$. The circuit contains resistance of $80 \Omega$ an inductor having inductive reactance $70 \Omega$ and a capacitor of capacitive reactance $130 \Omega$. The power factor of the circuit is $x$. The value of $x$ is

Accepted Answer

Given:
Source voltage, $V = 230$ V
Frequency, $f = 50$ Hz
Resistance, $R = 80~\Omega$
Inductive reactance, $X_L = 70~\Omega$
Capacitive reactance, $X_C = 130~\Omega$
Let us find the power factor step-by-step:
Step 1: Calculate Net Reactance
$ X = X_L - X_C = 70 - 130 = -60~\Omega $
Step 2: Calculate Impedance
$ Z = \sqrt{R^2 + X^2} = \sqrt{(80)^2 + (-60)^2} = \sqrt{6400 + 3600} = \sqrt{10000} = 100~\Omega $
Step 3: Power Factor Formula
Power factor, $x = \cos\phi = \dfrac{R}{Z}$
$ x = \frac{80}{100} = 0.8 $
Step 4: Correct Option
Option B: 0.8

Answer

0.4

Answer

0.8

Answer

0.6

Answer

0.9

AC fundamentals

A series LCR circuit is connected to an a.c. source of 230 \mathrm{~V}, 50 \mathrm{~Hz}. The circuit contains resistance of 80 \Omega an inductor having inductive reactance 70 \Omega and a capacitor of capacitive reactance 130 \Omega. The power factor of the circuit is x. The value of x is

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