## Parallel Circuits

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# Parallel Circuits

When a number of resistors are conducted in such a way that one end of each of them is joined to a common point and the other ends being joined to another common point, as shown in then resistors are said to be connected in parallel and such circuits are known as parallel circuits. In these circuits current is divided into as many paths as the number of resistances.Let the resistors R

_{1}and R

_{2}be connected in parallel, as shown in and the potential difference of V volts be applied across the circuit.

Since potential difference across each resistor is same and equal to potential difference applied across the circuit.

According to Ohm’s law

Current in resistor R

_{1}, I

_{1}=

__V__

R

_{1}

Current in resistor R

_{2}, I

_{2}=

__V__

R

_{2}

Current in resistor R

_{3}, I

_{3 }=

__V__

R

_{3}

_{ }

Adding expressions (i), (ii) and (iii) we get

I

_{1 }+ I

_{2}+ I

_{3}=

__V__+

__V__+

__V__

__R__

_{1}R

_{2 }R

_{3}

I

_{1 }+ I

_{2}+ I

_{3}= V (

__1__+

__1__+

__1__)

R

_{1}R

_{2 }R

_{3}

and since I

_{1 }+ I

_{2}+ I

_{3}= I, the total current flowing through the circuit

So I = I

_{1 }+ I

_{2}+ I

_{3 }= V (

__1__+

__1__+

__1__)

R

_{1}R

_{2 }R

_{3}

or

__I__=

__1__+

__1__+

__1__

V R

_{1}R

_{2 }R

_{3}

and since

__I__=

__1__where R is the equivalent resistance of the whole circuit

V R

__I__=

__1__+

__1__+

__1__

R R

_{1}R

_{2 }R

_{3}

Thus when a number of resistors are connected in parallel, the reciprocal of the equivalent resistance is given by the arithmetic sum of the reciprocals of their individual resistances.

In general if n resistors of resistance R1 , R2, R3.........Rn are connected in parallel, then equivalent resistance R of the circuit is given by

__I__=

__1__+

__1__+

__1__+................+

__1__

R R

_{1}R

_{2 }R

_{3 }Rn

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