Question

A circuit has two `"6 Ω"` resistors in parallel, given input current is 6A, What is the current at one resistor?

Answer 1

`"3 A"`

Explanation:

In a parellel connection voltage remains same but current divides at the junction.

`"V = iR"`

`"i" ∝ 1/"R" color(white)(...)[∵ "V = constant"]`

For two resistors in parellel of resistances `"R"_1` and `"R"_2`

`"i"_1 : "i"_2 = "R"_2 : "R"_1`

From above

`"i"_1 = "R"_2/("R"_1 + "R"_2) × "i"`

`"i"_2 = "R"_1/("R"_1 + "R"_2) xx "i"`

Where `"i"` is input current.

If resistances of both the resistors are same. Then,

`"i"_1 = "R"/("R + R") × "i" = "i"/2`

`"i"_2 = "R"/"R + R" × "i" = "i"/2`

So, we can conclude that if `"n"` number of resistors of same resistances are connected in parellel then the current flowing through each resistor is

`"i"_"R" = "Total input current"/"Number of resistors connected in parellel" = "i"/"n"`

Answer to your question

`"i"_"R" = "6 A"/2 = "3 A"`