Question

Design and draw voltage regulator to provide 4 to 10V variable output voltage using IC 7812.

Answer 1

Consider the following very simple scheme:

IC 7812 is a voltage regulator with the output voltage of $V_\text{IC7812}=12 \text{ V}$ (see the last two numbers after 78) and input voltage of 14.6 - 35VDC​. We need a variable output voltage 4 to 10 V, therefore, we can use a voltage divider:

$$R_{2}=R_1\frac{1}{V_\text{IC7812}/V_\text{out}-1},$$

which gives $R_2=5R_1$ for $V_\text{out}=10 \text{ V}$ and $R_2=0.5R_1$ for $V_\text{out}=4 \text{ V}$.

We can choose $R_1=10\space\Omega$ and a variable resistance $R_2$ that would provide resistances 5 to 50 Ω. Keep in mind that the load resistance must be many times higher than the resistance of the voltage divider, so you may prefer choosing another rheostat or potentiometer.