Technician A says damage can occur to solid-state circuitry if the charging voltage is allowed to get too high. Technician B says damage can occur if the vehicle is allowed to run with the battery disconnected. Who is correct?

Both Technicians A and B are correct

Explanation:

A solid-state circuitry is usually composed of semi-conductor materials. When a higher voltage than usual is introduced to the circuitry it can cause overheating and damage the various semi-conductor materials that compose the solid-state circuitry. So the technician A is correct.

Disconnecting a car batter while the vehicle is allowed to run can damage the electronic components in the car. Asides providing electricity to the car, the battery also shorts AC, spikes and transients to ground. If you remove the battery while the vehicle is running, the spikes and transients will simply be transferred to your vehicle's electronics and damage them. So the technician B is also correct.