Technician A says that in a series circuit the total resistance of the circuit is the sum of all the individual resistances within the circuit. Technician B says that in a series circuit the sum of the voltage drops across each resistance will always equal the source voltage. Who is correct?

Both technicians are correct

Explanation:

Because we are talking about a series circuit, both technicians are correct.

The total resistance of a series circuit is equal to the sum of each of all the individual resistances that make up the series circuit, just as technician A says. And similarly when adding the voltage in each of the resistences or components of the series circuit it should be equal to the source voltage, the voltage supplied to the circuit, which is what Technician B says.

For these reasons the answer is that both A and B are correct.