Is it true that the higher the resistance the higher voltage would drop?
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No. This is only true if the current stays the same.
Imagine a single resistor across a battery. Regardless of the battery voltage and the resistor value, the resistor has to drop all that voltage.
Now a imagine a constant current source instead of the battery. Now the higher the resistor the higher the voltage drop because the current source forces more power through the same resistor as R increases.