Derive a statement stating the relationship between the number of resistors,the effective resistance of the circuit & the total current in parallel?

if all resistors are in parallel and each is r ohms

i each = V/r
total current I = n V/r
so
I = V /(r/n)
so effective total resistance R = r/n

Well, here's a statement for you: "When you have a bunch of resistors having a little resistance party in parallel, the effective resistance of the circuit gets lower than a limbo dancer's backside, while the total current gets higher than a caffeine addict on roller skates!"

In more technical terms, the relationship can be stated as follows: In a parallel circuit, as the number of resistors increases, the effective resistance of the circuit decreases, while the total current flowing through the circuit increases. There you have it!

The relationship between the number of resistors, the effective resistance of the circuit, and the total current in a parallel circuit can be summarized by the following statement:

In a parallel circuit, the total resistance decreases as the number of resistors increases. Additionally, the total current in the circuit is equal to the sum of the currents flowing through each individual resistor.

To derive a statement stating the relationship between the number of resistors, the effective resistance of the circuit, and the total current in parallel, we can analyze the properties of resistors in parallel.

In a parallel circuit, the resistors are connected side by side, allowing multiple current paths for the flow of electricity. The relationship between the number of resistors, the effective resistance of the circuit, and the total current can be described using the following principles:

1. Effective Resistance (Req): In a parallel circuit, the total resistance is lower than the individual resistances. The effective resistance (Req) of the parallel circuit is given by the reciprocal of the sum of the reciprocals of the individual resistances.

Mathematically, if we have 'n' resistors (R1, R2, R3, ..., Rn) in parallel, the formula for effective resistance is:

1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

2. Total Current (It): In a parallel circuit, the total current is the sum of the individual currents flowing through each resistor. The total current is directly related to the sum of the reciprocal of the individual resistances.

Mathematically, if we have 'n' resistors (R1, R2, R3, ..., Rn) in parallel, the formula for total current is:

It = I1 + I2 + I3 + ... + In

Where I1, I2, I3, ..., In are the currents flowing through each resistor.

The statement that summarizes the relationship between the number of resistors, the effective resistance, and the total current in a parallel circuit is:

"In a parallel circuit, the effective resistance of the circuit is calculated by taking the reciprocal of the sum of the reciprocals of the individual resistances. The total current flowing through the circuit is the sum of the currents flowing through each resistor."