Consider a five-pointed star made of resistors as shown below. Each resistor has resistance R=6 Ω. Find the equivalent resistance in Ohms between the points A and B.
Details and assumptions
Note: Points ABCDE are labeled for easy reference if you need to use some combination of them in a solution.
Where is the picture?
cant post :(
answer is 7
To find the equivalent resistance between points A and B in the given star configuration of resistors, we can follow these steps:
1. Label each resistor for easier reference. Let's assume the resistors are labeled as follows:
R₁ - Top resistor
R₂ - Upper left resistor
R₃ - Upper right resistor
R₄ - Lower left resistor
R₅ - Lower right resistor
2. Identify the resistors that directly connect points A and B. In this case, R₁, R₂, and R₃ connect A and B.
3. Calculate the total resistance between points A and B as follows:
1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃
Rtotal = 1 / (1/R₁ + 1/R₂ + 1/R₃)
4. Since each resistor has the same resistance, R = 6 Ω, we can substitute R for each resistor:
Rtotal = 1 / (1/6 + 1/6 + 1/6)
5. Simplify the equation:
Rtotal = 1 / (3/6)
Rtotal = 1 / (1/2)
Rtotal = 2 Ω
Therefore, the equivalent resistance between points A and B is 2 Ω.