# AC Voltage Divider Calculator

A calculator to calculate the output voltage of an ac voltage divider is presented. The calculator computes the output voltage in polar form.

## Formula for the Output Voltage Voltage Divider Used in the Calculator

A voltage divider is shown below with input $V_{in}$ and output $V_{out}$. Using Kirchhoff's and Ohm's, it can easily be shown that
$V_{out} = \dfrac{Z_2}{Z_2+Z1} V_{in}$
or
$\dfrac{V_{out}}{V_{in}} = \dfrac{Z_2}{Z_2+Z1}$

## Example Using the Calculator

In the AC circuit below, we are given $v_{in} = 10 \angle 0^{\circ}$ , $R_1 = 100 \; \Omega$, $C = 0.47 \; \mu F$, $R_2 = 120 \; \Omega$ and $L = 20 \; mH$ , frequency $f = 2.5$ kHz.
Find the output voltage $V_{out}$ and the ratio $\dfrac{V_{out}}{V_{in}} = \dfrac{Z_2}{Z_2+Z_1}$. Let
$\dfrac{1}{Z_1} = \dfrac{1}{R_1} + j 2 \pi f C$ , resisitor $R_1$ and capacitor $C$ are in parallel
Use Parallel RC circuit Impedance Calculator to calculate $Z_1$ and obtain
$Z_1 = 80.45052 \; \Omega \angle -36.44^{\circ}$

$\dfrac{1}{Z_2} = \dfrac{1}{R_2} + \dfrac{1}{j 2 \pi f L }$ , resisitor $R_2$ and inductor $L$ are in parallel
Use Parallel RL circuit Impedance Calculator to calculate $Z_L$ and obtain
$Z_2 = 112.1004 \; \Omega \angle 20.91^{\circ}$
The above values for $Z_1$ and $Z_2$ are the default values for the calculator but of course you may change these values.
You may also use the complex to polar impedance converter to convert impedances that are in standrd complex form.

## Use of the calculator

Enter the input peak source voltage, the impedances $Z_1$ and $Z_2$ in polar form then press "calculate".
The calculator presented may be used to calculate the ratio and output voltages for any circuit that may be reduced to the basic circuit shown above.
The ratio and and output voltage are in polar form.

 $V_{in}$ = 10 V   Impedance $Z_1$ = 80.45   $\angle$ -36.44 $^{\circ}$ Impedance $Z_2$ = 112.10   $\angle$ 20.91 $^{\circ}$