Resistors are classified as series and parallel connections according to the method of connection.

### Series circuit

Three resistances r1, r2 and r3 are connected in series and a voltage V is given across all the resistances. Hence the current flowing through all the resistances is I . At this point the potential difference across each resistor will be different. V₁ and V2. Let V 3 be the voltage drop across each resistance respectively.

The given voltage V will be the sum of these voltage drops

That is V = v1 + v2 + v3 ->(1)

According to Ohm's law

V1 = Ir1

V2 = Ir2

V3 = Ir3

If this is entered into Equation (1).

V = Ir1 + Ir2 + Ir3

V = IR

Therefore

IR = Ir1 + Ir2 + Ir3

R = r1 + r2 + r3

### Parallel circuit

Three resistances r1, r2 and r3 are connected in parallel. Given. and voltage V to these. The potential difference across all resistances will be the same.

The current flowing through each resistor will be different and these will be i1, i2 and i3 respectively.

How to find the resistance in this circuit:

Total current : I = i1 + i2 + i3 -> (a)

According to Ohm's law I = V/R

I1 = V/r1

I2 = V/r2

I3 = V/r3

If this is entered into equation (a).

I = V/r1 + V/r2 + V/r3

I = V/R

Therefore

V/R = V/r1 + V/r2 + V/r3

Since the voltage V here is common

1/R = 1/r1 + 1/r2 + 1/r3

Two or more resistances connected back to back (end to end) is called a series circuit. Now the same current flows through all the resistances. The total resistance (effective resistance) is the sum of each.

A circuit in which two or more resistances are connected in parallel and a differential current flows through each is called a parallel circuit. The current in the circuit is the sum of the currents flowing through each resistance.

In series circuit, the effective resistance increases as the number of resistors connected increases. Effective resistance decreases as the number of resistors increases in a parallel circuit.

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