a coil o inductive reactance 31 ohm has a resistance o 8 ohm . It is placed in series with a condenser o capacitive reactance 25 ohm. the combination is connected to an AC source o 110 V . the power actor o the circuit is
Question
a coil o inductive reactance 31 ohm has a resistance o 8 ohm . It is placed in series with a condenser o capacitive reactance 25 ohm. the combination is connected to an AC source o 110 V . the power actor o the circuit is
Solution
The power factor of the circuit can be calculated using the formula:
Power Factor (PF) = R / Z
Where: R = Resistance Z = Impedance
First, we need to calculate the total impedance (Z) of the circuit. Since the coil and the condenser are in series, their reactances add up algebraically. The total reactance (X) is the difference between the inductive reactance (XL) and the capacitive reactance (XC), i.e., X = XL - XC.
Given: XL = 31 ohm XC = 25 ohm
So, X = XL - XC = 31 ohm - 25 ohm = 6 ohm
The impedance (Z) of a circuit with resistance (R) and reactance (X) is given by the Pythagorean theorem: Z = sqrt(R^2 + X^2)
Given: R = 8 ohm
So, Z = sqrt((8 ohm)^2 + (6 ohm)^2) = 10 ohm
Now, we can calculate the power factor:
PF = R / Z = 8 ohm / 10 ohm = 0.8
So, the power factor of the circuit is 0.8.
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