Question

Why is there a decrease in resistance when a parallel combination is used?

Answer 1

Hint: In a parallel combination the flow of current splits and makes the current pass through a greater cross sectional area than when the current passes through series. Since resistance is inversely proportional to the area of the cross section of the wire, then the resistance decreases.

Complete step by step solution:
Electrical resistance is defined as the property of a substance to oppose the flow of electric current in a circuit which is dependent upon variables such as mechanical stress, temperature, the area of cross section through which the current flows, and the length through which the current flows through the material. However, the electrical resistance offered by any object also depends on what material the object or the wire is made of; in other words resistivity of the given material. This property called resistivity is what makes any material a conductor or an insulator to electric current. Thus, the resistance of any object under standard pressure and temperature conditions is given by;
$R=\rho \dfrac{l}{A}$
Where, $R$ is the resistance we need to find of the given object, $l$ is the length the electric current traverses through the object, $A$ is the area of cross section of the object across which the current is distributed and $\rho $ is the constant called resistivity of the material with which the material is made of.
According to the question given to us we have current distributed in a parallel combination, thus exposing the current flow to greater cross sectional area to pass through. And since we know that the resistance offered by the wire is inversely proportional to the area of cross section of the wire through which the current passes, and directly proportional to length through which current passes, or in other words;
$R\propto \dfrac{1}{A}$
$R\propto l$
Therefore, as more and more resistors get added in parallel combinations, $A$ increases and $R$ decreases thus decreasing the net resistance. Also, as more and more resistors are added in series the length through which the current passes increases hence increasing the net resistance.

Note: As mentioned above electrical resistance is subject to a number of variables especially temperature and mechanical stresses which come into play in highly sensitive experiments. Also, in most non-ideal cases involving alloys of different metals or semiconductors the voltage and current across a resistor generally do not follow a linear relationship.