Three resistors each of resistance 12ohm are connected in the form of a triangle what is the equivalent resistance across any two vertices of the triangle
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The combination will make the resistor “triangle” equal to 8 ohms for each of the three possibilities (A-B, A-C and B-C). The way to calculate its equivalent resistance is to view the “triangle” as three identical networks.
Let’s analyze this network between points A and B. You have two 12 ohm resistors connected in series between points A and C. Therefore the total resistance between points A and C is 24 ohms. This 24 ohm equivalent resistance is then connected in parallel to the 12 ohm resistor connected between point A and B. The equivalent resistor just become simple to calculate since it is the same as to calculate two resistors in parallel:
Rt = (12 ohms X 24 ohms) /(12 ohms + 24 ohms) = 288 ohms square \ 36 ohms = 8 ohms.
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Let’s analyze this network between points A and B. You have two 12 ohm resistors connected in series between points A and C. Therefore the total resistance between points A and C is 24 ohms. This 24 ohm equivalent resistance is then connected in parallel to the 12 ohm resistor connected between point A and B. The equivalent resistor just become simple to calculate since it is the same as to calculate two resistors in parallel:
Rt = (12 ohms X 24 ohms) /(12 ohms + 24 ohms) = 288 ohms square \ 36 ohms = 8 ohms.
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Answer:
Between any two vertices you have two 12Ω resistors in series, the combination being in parallel with another 12Ω resistor. So, to calculate that:
Two in series: 2 × 12Ω = 24Ω
24Ω in parallel with 12Ω is (24×12)/(24+12) or 8Ω
The answer is 8Ω
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