Capacitor & Resistor

Form

Using default values of 230V at 50Hz and a 51Ω & 154µF.

Form
Supply Voltage Frequency Resistance Farads µF Password

Capacitive Reactance

Using default values of 230V at 50Hz and a 51Ω & 154µF.

X_{C} = \frac{1}{2πfC}

X_{C} = \frac{1}{2π x 50 x 154 {x10}^{-6}}

X_{C} = 20.67 Ω

Impedance

Using default values of 230V at 50Hz and a 51Ω & 154µF.

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

Z = \sqrt{51^{2} + {20.67}^{2}}

Z = \sqrt{2601 + 427.25}

Z = \sqrt{3028.25}

Z = 55.03 Ω

Power Factor

Using default values of 230V at 50Hz and a 51Ω & 154µF.

cosΦ = \frac{R}{Z}

cosΦ = \frac{51}{55.03}

cosΦ = 0.927 leading

{Cos}^{-1} 0.927 = 22.03° leading

Current

Using default values of 230V at 50Hz and a 51Ω & 154µF.

I = \frac{V}{Z}

I = \frac{230}{55.03} = 4.18 A

Current

Using default values of 230V at 50Hz and a 51Ω & 154µF.

I = \frac{V}{Z}

I = \frac{230}{55.03}

I = 4.18 A

Voltages

Using default values of 230V at 50Hz and a 51Ω & 154µF.

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

V_{R} = I x R

V_{R} = 4.18 x 51 = 213.18 V

V_{C} = I x X_{C}

V_{C} = 4.18 x 20.67 = 86.4006 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_{C}}^{2}}

V_{Supply} = \sqrt{{213.18}^{2} + {86.4006}^{2}}

V_{Supply} = \sqrt{45445.7124 + 7465.06368036}

V_{Supply} = \sqrt{52910.77608036}

V_{Supply} = 230.02 V

W, VA & VAR

Using default values of 230V at 50Hz and a 51Ω & 154µF.

Power = I^{2} R

Power = {4.18}^{2} x 51 = 891 W

VA = V x A

VA = 230 x 4.18 = 961.4 VA

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

{VA}_{r} = \sqrt{{961.4}^{2} - 891^{2}}

{VA}_{r} = \sqrt{924289.96 - 793881}

{VA}_{r} = \sqrt{130408.96} = 361.12 {VA}_{r}

Phasor Diagram

Impedance Triangle

Power Triangle