The effective resistance of resistors connected in parallel can be calculated using the formula:
1/Re = 1/R1 + 1/R2 + 1/R3 + ...
In this case, we have three equal resistances connected in parallel, each with a resistance of r. So, the formula becomes:
1/Re = 1/r + 1/r + 1/r
Simplifying this equation, we get:
1/Re = 3/r
To find the effective resistance, we take the reciprocal of both sides:
Re = r/3
So, the correct answer is option 2: r/3.