Three resistors, each of resistance 6 Ω, are connected in such a way that that they form the three sides of a triangle. What is the equivalent resistance between any two vertices of the triangle?
Re = 6*(6+6)/(6+6+6) = 6*12/18 = 72/18 =
4 Ohms.
To find the equivalent resistance between any two vertices of the triangle, we can use the concept of "resistors in parallel" and "resistors in series".
In this case, since the resistors are connected in a triangular configuration, we can consider each resistor as being in parallel with the other two resistors. This means that the equivalent resistance between any two vertices of the triangle is the total resistance when the three resistors are connected in parallel.
To calculate the equivalent resistance for resistors connected in parallel, we use the formula:
1/Req = 1/R1 + 1/R2 + 1/R3 + ...
In this case, since all three resistors are equal (6 Ω), we can substitute the values into the formula:
1/Req = 1/6 Ω + 1/6 Ω + 1/6 Ω
Adding the fractions together gives:
1/Req = 3/6 Ω
Simplifying the fraction:
1/Req = 1/2 Ω
To isolate Req, we take the reciprocal of both sides:
Req = 2 Ω
Therefore, the equivalent resistance between any two vertices of the triangle is 2 Ω.