Calculate R_i Of A Power Source

Every power source has some internal resistance, no matter whether it is a lab power supply, the power supply of your circuit or a battery. Even if it is neglectable small.
This program helps you to determine the internal resistance of a power source. And it calculates the EMF., which is the voltage of the power source when there is absolutely no load on it.

Before you can calculate the internal resistance and the EMF you need to make 2 measurements, with different output current. In both cases you'll need to know the voltage at the output terminals of the power supply and the current delivered by the power supply. The accuracy of the calculation depends on the difference between the two currents. The larger the difference, the better the result will be.
The terminal voltage of the first measurement is called U1, while the current flowing during measurement one is called I1. It goes without saying that U2 and I2 are the values for the second measurement. Then the following two formulas apply:

R_i = (U1-U2) / (I2 - I1)

The EMF ε = I2(R_i + U2 / I2) or ε = U2 + I2 x R_i

The Program

	000–
h LBL A	001–	25 13 11
STO 4	002–	23 4
g R↓	003–	15 22
STO 3	004–	23 3
g R↓	005–	15 22
STO 2	006–	23 2
g R↓	007–	15 22
STO 1	008–	23 1
RCL 3	009–	24 3
–	010–	41
RCL 4	011–	24 4
RCL 2	012–	24 2
–	013–	41
÷	014–	71
ENTER↓	015–	31
ENTER↓	016–	31
RCL 4	017–	24 4
×	018–	61
RCL 3	019–	24 3
+	020–	51
h RTN	021–	25 12

Examples

Before we can make the calculation we need to make a few measurements. Measure the voltage at the output terminals with a low load, call this U1. Also make a current measurement and call this I1.
Then with a significantly higher load measure the terminal voltage again and call that U2. Also measure the current and call it I2.
Make sure you make no large measurement errors. Measure the voltage directly at the output terminals of the power source. Do not measure the voltage behind the Ampere meter, because that would add the shunt resistor of this Ampere meter to R_i!

Let's assume U1 = 9.975V, I1 = 9.975mA, U2 = 9.756V and I2 = 97.56mA

Put all measurements on the stack:

U1 ENTER🠕 I1 ENTER🠕 U2 ENTER🠕 I2 ENTER🠕
And finally press the A key to start the calculation. The calculator will display the value of the EMF ε first. The result is in Volts. After pressing X⇋Y you'll see the internal resistance R_i of the power supply.

In the case of our example above ε will be 10V, and R_i is 2.5Ω.

Register Use

U1 is stored in R1.
I1 is stored in R2.
U2 is stored in R3.
I2 is stored in R4.

X returnes ε.
Y returnes R_i.