WEBVTT

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Let us discuss current division rule

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This rule is very important, and widely
used in the field of electric engineering

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Actually, this rule finds application, when
we have to find the current passing through

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each impedance when, these are connected in parallel. Let us
say, two impedances, Z1, and Z2, are connected in parallel

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A current, I, passes through the system. This, I,
is then divided into I1, and I2, at this junction

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I1, and I2 pass through Z1, and Z2 respectively. Our aim
is to determine, I1, and I2 in terms of, I, Z1, and Z2

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As, Z1, and Z2 are connected in parallel,
voltage drop across each will be, same

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Hence, we can write, I1 into Z1 equal to, I2 into
Z2, and this is voltage drop across, Z1, or Z2

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As total current, I, is divided into I1, and
I2, we can write, I, equals to I1, plus, I2

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Say, this equation is 2. From, equation 1,
we get, I2 equals to, I1 Z1 divided by Z2

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Computing, this expression of I2 in equation 2, we
get, I, equals to I1, plus, I1 into Z1 divided by, Z2

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It implies, I, Z2 equals to I1, Z2, plus
I1, Z1, equals to I1 into, Z2 plus Z1

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Therefore, I1 equals I, Z2 divided by Z1 plus Z2. Similarly,
we can show, I2 equals I, Z1 divided by Z1 plus Z2

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From, these expressions of current, we can conclude
that, current in any of the parallel paths, is

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total current into impedance of the path through which the current
is not determined, divided by sum of impedance of parallel paths

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Hope you got a basic idea. Thank you