(i) Current in the coil and phase angle of this current:

First, we need to calculate the inductive reactance (XL) of the coil. The formula for inductive reactance is XL = 2πfL, where f is the frequency and L is the inductance.

XL = 2π * 50Hz * 140mH = 2π * 50 * 0.14 = 44Ω

The coil is a combination of resistance (R) and inductive reactance (XL), so we can use Pythagoras' theorem to find the total impedance (Z) of the coil.

Z = √(R² + XL²) = √(10² + 44²) = √1936 = 44Ω

The current in the coil (I) can be found using Ohm's law, I = V/Z, where V is the voltage.

I = 230V / 44Ω = 5.23A

The phase angle (φ) can be found using the formula φ = arctan(XL/R).

φ = arctan(44/10) = 77.47°

(ii) Supply current:

The supply current is the same as the current in the coil, as they are connected in parallel. So, the supply current is 5.23A.

(iii) Circuit impedance:

The total circuit impedance (ZT) can be found using the formula for parallel resistances, 1/ZT = 1/Z1 + 1/Z2.

1/ZT = 1/44Ω + 1/260Ω = 0.0227 + 0.00385 = 0.02655

ZT = 1 / 0.02655 = 37.7Ω

(iv) Power factor:

The power factor (PF) can be found using the formula PF = cos(φ).

PF = cos(77.47°) = 0.22

(v) Power consumed:

The power consumed (P) can be found using the formula P = IVcos(φ), where I is the current, V is the voltage, and φ is the phase angle.

P = 5.23A * 230V * 0.22 = 264.9W

Question

(i) Current in the coil and phase angle of this current:

First, we need to calculate the inductive reactance (XL) of the coil. The formula for inductive reactance is XL = 2πfL, where f is the frequency and L is the inductance.

XL = 2π * 50Hz * 140mH = 2π * 50 * 0.14 = 44Ω

The coil is a combination of resistance (R) and inductive reactance (XL), so we can use Pythagoras' theorem to find the total impedance (Z) of the coil.

Z = √(R² + XL²) = √(10² + 44²) = √1936 = 44Ω

The current in the coil (I) can be found using Ohm's law, I = V/Z, where V is the voltage.

I = 230V / 44Ω = 5.23A

The phase angle (φ) can be found using the formula φ = arctan(XL/R).

φ = arctan(44/10) = 77.47°

(ii) Supply current:

The supply current is the same as the current in the coil, as they are connected in parallel. So, the supply current is 5.23A.

(iii) Circuit impedance:

The total circuit impedance (ZT) can be found using the formula for parallel resistances, 1/ZT = 1/Z1 + 1/Z2.

1/ZT = 1/44Ω + 1/260Ω = 0.0227 + 0.00385 = 0.02655

ZT = 1 / 0.02655 = 37.7Ω

(iv) Power factor:

The power factor (PF) can be found using the formula PF = cos(φ).

PF = cos(77.47°) = 0.22

(v) Power consumed:

The power consumed (P) can be found using the formula P = IVcos(φ), where I is the current, V is the voltage, and φ is the phase angle.

P = 5.23A * 230V * 0.22 = 264.9W

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