I've been asked to calculate the theoretical resistance of R1 in the shown circuit. The information that I've been given is that the relay needs 60 mA and 12V. I've also been told that the transistor's hFE/Beta value is 20 and that the voltage drop between the base and emitter is 0.7 V. I've tried calculating the resistance of R1, but when I do I don't seem to use all of the information given which leads me to believe that I am doing it wrong. Furthermore, I am a bit confused as to what is meant by the term theoretical resistance of R1.

If anyone could lead me in the right direction I would greatly appreciate it.

## Best Answer

You don't need to use the 12V supply voltage for anything. It's not uncommon for questions to include some extraneous information.

If you assume the input to be a (theoretical) value the same as the MCU supply voltage it might be 5.0, 3.3, 2.5, 1.8 or something else entirely. A reasonable assumption might be 5.0, but you should state your assumption clearly.

In reality you would want to use a much lower value for the resistor than the value you will calculate above using Ohm's law and the nominal Vbe drop, to ensure deep saturation for the transistor and to account for the voltage drop in the MCU output transistor, voltage tolerances, temperature effects on the transistor, MCU output circuitry and relay coil etc.