## PARALLEL CIRCUIT

When two or more resistors are connected across a common point so that same current flows through different paths they are said to be connected in parallel. Suppose three resistors R_{1}, R_{2} and R_{3} are joined in parallel as shown in figure and let the potential difference applied across point A and B be V.

Let I be the current reaching point A from the battery and I_{1}, I_{2} and I_{3} be the current passing through resistors R_{1}, R_{2} and R_{3} respectively. Here it is clear that total current:

I = I_{1} + I_{2} + I_{3} (1)

According to Ohm's law

V = I_{1}R_{1} = I_{2}R_{2} = I_{3}R_{3}

or I_{1} = , I_{2} = and I_{3} =

If R_{p} is the resultant resistance of the parallel circuit, then

V = IR_{p}

or I =

By putting the values of I, I_{1}, I_{2} and I_{3} in equation (1), we get

or

So, when the resistors are joined in parallel the reciprocal of total resistance of a number of resistors is equal to the sum total of the reciprocal of all the individual resistors.

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