That is why I use 2 relays (high & dim) to operate my headlights. By the time the power goes through the dash switch, the dimmer switch, and a handful of the "bullet" connectors, the resulting voltage is inadequate, thus the 4 volts you mentioned. Now my headlights are as bright as new. It doesn't take much resistance to soak up voltage In Ohm's Law E=IR. Thus E (voltage) is the product of I (amperage) and resistance (R). My unit is mounted at the left front under the hood where the main headlight junction is located. The relays are operated by the original circuit, and provide full battery power to the headlights so after dark driving is safe.