Reactance LR

Reactance L & R

Form

Using randomly chosen values of 230V at 50Hz with 41Ω & 67mH.

Form
Supply Voltage Frequency Resistance Inductance (mHenries) Password

Inductive Reactance

Using randomly chosen values of 230V at 50Hz with 41Ω & 67mH.

X_{L} = 2πfL

X_{L} = 2π x 
			50 x 67{x10}^{-3}

X_{L} = 21.05 Ω

Impedance

Using randomly chosen values of 230V at 50Hz with 41Ω & 67mH.

Z = \sqrt{R^{2} + X^{2}}

Z = \sqrt{41^{2} + {21.05}^{2}}

Z = \sqrt{1681 + 443.1}

Z = \sqrt{2124.1}

Z = 46.09 Ω

Power Factor

Using randomly chosen values of 230V at 50Hz with 41Ω & 67mH.

cosΦ = \frac{R}{Z}

cosΦ = \frac{41}{46.09}

cosΦ = 0.89 lagging

{Cos}^{-1} 0.89 = 27.13 lagging

Current

Using randomly chosen values of 230V at 50Hz with 41Ω & 67mH.

I = \frac{V}{Z}

I = \frac{230}{46.09}

I = 4.99 A

Voltages

Using randomly chosen values of 230V at 50Hz with 41Ω & 67mH.

Using Ohm's Law we can calculate the voltages present across each component as follows.

V_{R} = I x R

V_{R} = 4.99 x 41 = 204.59 V

V_{L} = I x L

V_{L} = 4.99 x 21.05 = 105.0395 V

Unless one of either resistance or inductance is zero the sum of these two voltages does not add up to the supply voltage.

If we were to draw the two voltage values at right angles to each other then the resulting hypotenuse would equal the supply voltage (or very close to it allowing for rounding errors).

We'll now check.

V_{Supply} = \sqrt{{V_{R}}^{2} + {V_{L}}^{2}}

V_{Supply} = \sqrt{{204.59}^{2} + {105.0395}^{2}}

V_{Supply} = \sqrt{41857.0681 + 11033.29656025}

V_{Supply} = \sqrt{52890.36466025}

V_{Supply} = 229.98 V

W, VA & VAR

Using randomly chosen values of 230V at 50Hz with 41Ω & 67mH.

Power = I^{2} R

Power = {4.99}^{2} x 41

Power = 1021 W

VA = V x A

VA = 230 x 4.99

VA = 1147.7 VA

{VA}_{r} = \sqrt{{VA}^{2} - W^{2}}

{VA}_{r} = \sqrt{{1147.7}^{2} - 1021^{2}}

{VA}_{r} = \sqrt{1317215.29 - 1042441}

{VA}_{r} = \sqrt{274774.29}

{VA}_{r} = 524.19 {VA}_{r}

Phasor Diagram

Impedance Triangle

Power Triangle