JEEZ! Now we're talking theory vs. potential? The guy just wants to know if his ballast resistor is good or needs to be replaced. With the points open, the MEASURED voltage will be the same at both ends of the resistor because a typical VOM is not sensitive enough to measure the drop created by the meter itself. With the points closed the circuit will be complete and there will be current flowing through the resistor. The MEASURED voltage will be different now on the downstream end of the resistor. No need to pull out degrees and certificates and measure them. Help the OP fix his car!