Let the resistance of an electrical component remain constant while the potential difference across the two ends of the component decreases to the half of it former value. What change will it occur in the current through it?

The current through it will also decrease to half of its former value because according to Ohm's law the current flowing through a resistor is directly proportional to the potential difference applied across its ends provided that the temperature and some other necessary conditions remain constant.

This is mathematically represented as follows;

The current is thus given as

if R is constant and V is reduced to half, then we have the following;

Simplifying further we obtain

Equation (3) shows that the current I is also reduced to half.