** Series combination**

In a series connection, all resistors are connected end to end (lengthwise) with each other. In such connections, the total resistance of the circuit increases. The given figure shows three resistors of resistance R_{1}, R_{2}, and R_{3} respectively connected in a series with each other.

The equivalent resistance of the resistors connected in series is given by the algebraic sum of their individual resistances.

Equivalent resistance or R_{S} = R_{1} + R_{2} + R_{3}

**derivation of it :**

Suppose, there are ‘n’ resistances connected in series. The resistances are: R _{ 1 } , R _{ 2 } , R _{ 3 } , R _{ 4 } …… R _{ n } . Voltage ‘V’ is applied across the ends of the connection. Let I current flown through the series of resistances.

Since, current I will be same through all the resistances and the sum of voltage drop across all the resistances gives us the voltage ‘V’. Therefore,

V = IR _{ 1 } + IR _{ 2 } + IR _{ 3 } + IR _{ 4 } +………….. IR _{ n }

=> V = I(R _{ 1 } + R _{ 2 } + R _{ 3 } + R _{ 4 } +………….. R _{ n } )

Thus, the series of resistances can be summed up and the equivalent resistance of the circuit is the sum of the resistances.

Therefore, V = IR _{ s }

Where, R _{ s } = R _{ 1 } + R _{ 2 } + R _{ 3 } + R _{ 4 } +………….. R _{ n }

**Parallel combination **

Here three resistances are connected in parallel.In this case the potential difference across the ends of all the resistances will be same and it will be equal to the voltage of the battery used.

Suppose the total current flowing through the circuit=I,then the current passing through resistance

Current through and current through

**power :**

Electrical **Energy** is *E* = *P* × *t*