Question

Why does the sum total of resistances in parallel decrease with the increase in number or resistors?

Answer 1

As additional resistors are added, additional current paths are provided, increasing the total current. Ohms law now prevails. The voltage across the resistors is the same. When current increases, the resistance has decreased.

Answer 2

as we know,
I=I1+I2=I3
here, V=IR
So,
V/R=V1/R1+V2/R2+V3/R3;
Here, V=V1=V2=V3
From above,
V/R=V(1/R1+1/R2+1/R3)
where 'V' will be canceled,
as a result,
1/R=1/R1+1/R2+1/R3
WHICH PROVES THAT WITH THE INCREASE IS RESISTOR THE RESISTANCE DECREASE OF WHOLE CIRCUIT....
OK friend

Answer 3

but how is V = V1 = V2 = V3?

Answer 4

Note that a voltmeter placed between ground and V or V1, or V2, or V3 will indicate the same voltage. That is how.