Resistance of A System Of Resistors

RESISTANCE OF A SYSTEM OF RESISTORS

When two or more resistance connected with each other in a circuit is called combination of resistance. There are two combination of resistance.

Resistors in Series

Two resistors are said to be combined in series if they carry the same current. In such circuits, the voltage across each resistor is different. In a series connection, if any resistor is broken or a fault occurs, then the entire circuit is turned off. 

For the above circuit, the total resistance is given as:

Rtotal = R1 + R2

Example

A resistor with an electrical resistance value of 100 ohms is connected to another with a resistance value of 200 ohms. The two resistances are connected in series. What is the total resistance across the system?

Here, R1 = 100 Ω and R2= 200 Ω

Rtotal = 100 + 200 = 300 Ω

 

If there is n no. of resistance in circuit, the total resistance is given as:

Rtotal = R1 + R2 + ….. + Rn

Resistors in Parallel

 Two resistors are said to be combined in parallel if the same potential difference is applied to them.  In such circuits, the current is branched out and recombined when branches meet at a common point. A resistor or any other component can be connected or disconnected easily without affecting other elements in a parallel circuit.

The sum of reciprocals of resistance of an individual resistor is the total reciprocal resistance of the system.

Example

A resistor with an electrical resistance value of 100 ohms is connected to another with a resistance value of 200 ohms. The two resistances are connected in parallel. What is the total resistance across the system?