Question

A coil having resistance of 7 ohms and inductance of 31.8 mh is connected to 230v,50hz supply.calculate 1. The circuit current 2.the phase angle, 3.power factor, 4 the power consumed

Answer 1

(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:

• V = 230 V.

Substitute into equation 2

• I = 230/12.19
• I = 18.87 A

(2) To calculate the phase angle, we use the formula below.

• ∅ = tan⁻¹(2πfL/R)............... Equation 3

Where:

• ∅ = Phase angle.

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:

• pf = power factor.

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:

• P = The power consumed

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

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