Question

explain the parallel combination of resistors and derive the formula of equivalent resistance​

Answer 1

In series combination, resister are connected end to end and current has a single path through the circuit but the potential difference varies across each resistor. Thus we can write as,

V = V1 + V2 + V3

according to Ohm's law V = IR So,

V1 = I R1, V2 = I R2, V3 = I R3

V = I R1 + I R2 + I R3

V = I(R1+R2+R3)

V =IRe

All the individual resistances become equal to the equivalent resistance.

or Re = R1 + R2 + R3......Rn

In parallel combination, each resistor'sone is connected to the positive terminal while the other end is connected to a negative terminal. The potential difference across each resistance is the same and the current passing through them is different.

V = V1 =V2=V3

I = I1+ I2+I3

Current throught each resistor will be:

I1= V/R1 , I2 = V/R2 = I3 = V/R3

I = V (1/R1+ 1/R2+1/R3)

In case of equivalent resistance I=V/Re

V/Re = V (1/R1+ 1/R2+1/R3)

So the equivalnet resistance is the sum of all resistances

1/Re = 1/R1+ 1/R2+1/R3

Answer 2

Answer:

Resistors in parallel -

Resistors are said to be connected together in parallel when both of their terminals are respectively connected to each terminal of the other resistor or resistors.

In a parallel resistor network the circuit current can take more than one path as there are multiple paths for the current. Then parallel circuits are classed as current dividers.

So we can define a parallel resistive circuit as one where the resistors are connected to the same two points (or nodes) and is identified by the fact that it has more than one current path connected to a common voltage source. Then in our parallel resistor example below the voltage across resistor R1 equals the voltage across resistor R2 which equals the voltage across R3 and which equals the supply voltage.

Explanation:

Resistance in Parallel

we show 3 resistors connected 'in parallel' with one another. In this  case, the current flowing is divided among the 3 resistors:

i = i1 + i2 + i3

However, the potential difference across any resistors  is the same, namely

i1 R1 = i2 R2 = 13 R3

These equations can be thought of as determining the currents i1, i2, i3.

Substituting, We have

i = ( V/R1 + V/R2 + V/R3 ) = V / R 

or

1/R1 + 1/R2 + 1/R3 = 1 / R. 

Similarly, For n number of resistors connected in parallel,

    

The Total Equivalent resistance = 1/R1 + 1/ R2 +.......+ 1/Rn = 1 / R.