Question

A coil

circuit resistance 15 ohm and inductances 0.05 Henry is connected in parallel with a non inductive resistance of 20 ohm find current age branch of the current total current is applied phase angle and phase power factor combination when a voltage 20 volts 850 parallel power consumed in the circuit
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Answer 1

Branch currents: I1 = 0.92 A, I2 = 1.0 A

Total current: I_total = 1.92 A

Phase angle: φ = 18.7 degrees

Power factor: pf = 0.946

Calculate total impedance (Z_parallel):

Coil impedance (Z1) = √(R1^2 + (2πfL1)^2) = √(15^2 + (2π * 50 * 0.05)^2) = 21.7 ohms (assuming 50 Hz frequency)

Z_parallel = 1 / (1/Z1 + 1/R2) = 1 / (1/21.7 + 1/20) = 8.47 ohms

Calculate branch currents (I1, I2):

I1 = V / Z1 = 20 V / 21.7 ohms = 0.92 A (coil current)

- I2 = V / R2 = 20 V / 20 ohms = 1.0 A (non-inductive current)

Calculate total current (I_total):

I_total = I1 + I2 = 0.92 A + 1.0 A = 1.92 A

Calculate phase angle (φ):

φ = arctangent(Z1's imaginary part / Z1's real part) = arctangent((2πfL1) / R1) = arctangent((2π * 50 * 0.05) / 15) = 18.7 degrees

Calculate power factor (pf):

pf = cos(φ) = cos(18.7 degrees) = 0.946