(1) The current in the circuit is 18.87 A,
(2) The phase angle is 54.97°
(3) The power factor is 0.574
(4) The power consumed is 2491.2 W
(1) To calculate the current in the circuit, first, we need to find the overall impedance of the circuit.
We can calculate the overall impendence of the circuit using the formula below.
- Z = √[R²+(2πfL)²]........................ Equation 1
Where:
- R = resistance of the coil
- f = Frequency
- L = Inductance of the coil
- Z = Overall impedance of the circuit
From the question,
Given:
- R = 7 ohms
- L = 31.8 mH = 0.0318 H
- f = 50 Hz
- π = 3.14
Substitute these values into equation 1
- Z = √[7²+(2×3.14×50×0.0318)²]
- Z = √(49+99.7)
- Z = √(148.7)
- Z = 12.19 ohms.
Therefore we use the formula below to calculate the current in the circuit.
- I = V/Z.................. Equation 2
Where:
- V = Voltage
- I = current in the circuit.
Given:
Substitute into equation 2
(2) To calculate the phase angle, we use the formula below.
- ∅ = tan⁻¹(2πfL/R)............... Equation 3
Where:
Substitute into equation 3
- ∅ = tan⁻¹(2×3.14×50×0.0318/7)
- ∅ = tan⁻¹(9.9852/7)
- ∅ = tan⁻¹(1.426)
- ∅ = 54.97°
(3) To calculate the power factor, we use the formula below.
- pf = cos∅............ Equation 4
Where:
Substitute the value of ∅ into equation 4
- pf = cos(54.97°)
- pf = 0.574.
(4) And Finally to calculate the power consumed we use the formula below.
- P = V×I×pf................ Equation 5
Where:
Substitute the values into equation 5
- P = 230(18.87)(0.574)
- P = 2491.22 W
Hence, (1) The current in the circuit is 18.87 A, (2) The phase angle is 54.97° (3) The power factor is 0.574 (4) The power consumed is 2491.2 W
Learn more about Impedance here: brainly.com/question/13134405
