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23rd March 2016, 10:47 AM
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Join Date: May 2012
Re: IIT JEE equivalent resistance

When two or more resistors are connected together as are the light bulbs, they are said to be in series.

Series Connection of registers

The potential difference applied across the series combination of resistors will divide between the resistors.



The voltage drop from a to b equals IR1 and the voltage drop from b to c equals IR2, the voltage drop from a to c is potential difference across series combination of resistors

Therefore, you can replace the two resistors in series with a single resistor having an equivalent resistance Req , where equivalent resistance series combination of resistors

The resistance Req is equivalent to the series combination R1 + R2 in the sense that the circuit current is unchanged when Req replaces R1 + R2.

The equivalent resistance of three or more resistors connected in series is equivalent resistance of three or more resistors connected in series

This relationship indicates that the equivalent resistance of a series connection of resistors is always greater than any individual resistance.

Parallel system of registers

Now consider two resistors connected in parallel, as shown in Figure




When the current I reaches point a in called a junction, it splits into two parts, with I1 going through R1 and I2 going through R2.

A junction is any point in a circuit where a current can split (just as your group might split up and leave the arena through several doors, as described earlier.)

This split results in less current in each individual resistor than the current leaving the battery.

Because charge must be conserved, the current I that enters point a must equal the total current leaving that point: total current in parallel combination of resistors

The potential differences across the resistors are the same, the expression ΔV =IR gives potential differences across parallel combination of resistors

1/Req =1/R1+ 1/R2 +1/R3 ……………


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