Since series voltage drops are proportional to the resistances, a very small R in series with a much larger R has a considerably large IR drop.

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In a series circuit, the voltage drop across a smaller resistance (R) is less than the voltage drop across a larger resistance, given that the current (I) is the same through all components. The voltage drop (V) across a resistor in a series circuit is given by Ohm's Law (V=IR), so a smaller resistance results in a smaller voltage drop.

Since Series Voltage Drops Are Proportional to the Resistances, a Very