Formula for Resistance in Parallel Connection:

When two or more resistors are connected in parallel, the total resistance of the circuit can be calculated using the following formula:

1/R(total) = 1/R(1) + 1/R(2) + 1/R(3) + … + 1/R(n)

where R(total) is the total resistance of the circuit, R(1), R(2), R(3), …, and R(n) are the resistances of each individual resistor.

Explanation:

When resistors are connected in parallel, each resistor has the same voltage across it. This means that the current through each resistor is different, depending on its resistance value. The total current through the circuit is equal to the sum of the currents through each resistor.

The total resistance of the circuit is the inverse of the sum of the reciprocals of each individual resistor's resistance. This formula can be derived from Ohm's law, which states that the current through a resistor is equal to the voltage across it divided by its resistance.

Example:

Suppose we have three resistors with values of 2 ohms, 4 ohms, and 6 ohms, connected in parallel. To find the total resistance of the circuit, we can use the formula:

1/R(total) = 1/2 + 1/4 + 1/6

1/R(total) = 0.5 + 0.25 + 0.167

1/R(total) = 0.917

R(total) = 1/0.917

R(total) = 1.09 ohms

Therefore, the total resistance of the circuit is 1.09 ohms.

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