8 resistors were connected 2 in series in 4 parallel branches. Derive the formula for calculating
| December 27, 2020 | education
8 resistors were connected 2 in series in 4 parallel branches. Derive the formula for calculating the total resistance for this connection.
Let’s denote the resistance of one resistor through R, so in each parallel branch there are 2 resistors, then the resistance of the branch will be equal to:
Rv = R + R = 2R.
The total resistance Rs will be (four parallel branches):
1 / Rs = 1 / Rv + 1 / Rv + 1 / Rv + 1 / Rv = 4 / Rv
Rs = Rv / 4 = 2R / 4 = R / 2.
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