# Resistors in Parallel

## Parallel Combination Of Resistors

R_{1}, R_{2} and R_{3} are three resistors connected across voltage source V. I_{1}, I_{2} and I_{3} are three current following in R_{1}, R_{2} and R_{3} respectively. It is the total current of supply source, as shown in the fig.

From the fig we understand that

*I _{T} = I_{1} + I_{2} + I_{3}*

We know that

*V=IR---> (1)*

*I = V/R--> (2)*

Put eq (2) in eq (1) we get

Dividing Both Sides by V we get

In General

Where n = 1,2,3,4,..........

## RESISTORS IN PARALLEL CHARACTERSTICs

- There are same voltages across each resistor in parallel ckt.
*V*_{T}= V_{1}= V_{2}= V_{3} - In each resistor the flow of current depends on the value of the resistor is high so small amount of current in that resistor as compare to that resistor whose value is less.
- The total current is equal to the sum of that current which flows in each resistor.
*I*_{T}= I_{1}+ I_{2}+ I_{3} - The total ckt resistance is equal to the sum of conductance of ckt. OR The total ckt resistance is equal to the sum of reciprocal of the ckt.
*OR**G*_{T}=G_{1}+G_{2}+G_{3} - If we increase the resistor in that ckt so the total resistance will be decrease
- As there are different path for the current so if fault is occur in a resistor, so the operation of the other resistor is continue.
- In that ckt the amount of the total resistance is also less than the amount of small resistor of the ckt.
- The path of the current flow is equal to parallel path of the ckt.
- The total power and energies equal to the sum of each path.
- These ckt are used commonly.

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