Question

derive an expression for the effective resistance of three R1, R2, R3, connected in parallel in an electric circuit​

Answer 1

Answer:

we show 3 resistors connected 'in parallel' with one another. In this case, the current flowing into P is divided among the 3 resistors

i = i1 + i2 + i3

However, the potential difference across any resistors is the same, namely

i1 R1 = i2 R2 = 13 R3

These equations can be thought of as determining the currents i1, i2, i3.

Substituting, We have

i = ( V/R1 + V/R2 + V/R3 ) = V / R

or

1/R1 + 1/R2 + 1/R3 = 1 / R.

Similarly, For n number of resistors connected in parallel,

The Total Equivalent resistance = 1/R1 + 1/ R2 +.......+ 1/Rn = 1 / R.

Explanation:

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Answer 2

Answer:

If two resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R / 2. Similarly, if three resistors of equal resistance R are connected in parallel combination then the equivalent resistance of the combination is R / 3.

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