The capacitive reactance of a capacitor can be used in a voltage divider from which we can design a transformerless power supplies as the one shown in figure bellow Supposing a resistive load we can calculate C and R using the next formulas:

**Formula 1**

Calculating R:

R = V / I

**Where: **

V is voltage across the load in volts (V)

I is the current in the load in amperes (A)

R is the load resistance in ohm (Ω)

Note: V and I are root mean square values (rms).

**Formula 2 **

Impedance:

Z = Vin / I

**Where: **

Z is the circuit impedance in ohm (Ω)

Vin is the input voltage in volts (V)

I is the total circuit current or load current in amperes (A)

**Formula 3 **

Capacitive reactance:

**Where:**

Xc is the capacitive reactance of the used capacitor in farads (F)

Z is the circuit impedance in ohm (Ω)

R is the load resistance in ohm (Ω)

**Formula 4**

**Where:**

C is the capacitance in microfarads (uF)

π is 3.1416

f is the AC power line frequency in hertz (Hz)

Xc is the capacitive reactance in ohm (Ω)

**Application example: **

Determine the capacitance of C in the circuit shown in figure 77 to power the 12 V x 50 mA lamp from the 117 V x 60 Hz power line.

**Data: **

V = 12 V

Vin = 117 V

I = 0.02 A (20 mA)

f = 60 Hz

C = ?

**a) Calculating R (formula1)**

R = 12/0.02 = 600 Ω

**b) Determining Z (formula 2)**

Z = 117/0.02 = 5 850 Ω

**c) Now, Xc can be found using formula 3:**

Xc = √[(5,850)^{2} - (600)^{2}] = √[31.9 x 10^{6} - 0.36 x 10^{6}] = √[31.56 x 10^{6} ] = 5 618 Ω

**d) Finding C (formula 4):**

C = 10^{6} / (2 x 3.14 x 60 x 5,618) = 10^{6} / 2.116 x 10^{6} = 1 / 2.116 = 0.47 µF or 470 nF