What resistance values can be obtained by connecting three resistors in all possible ways

| April 22, 2021 | education

What resistance values can be obtained by connecting three resistors in all possible ways, if the resistance of each is 6 ohms? What resistance values can be obtained by connecting three resistors in all possible ways, if the resistance of each is 6 ohms?

Given:

R = 6 Ohm – resistance of each resistor;

n = 3 is the number of resistors.

It is required to determine what resistance values ​​can be obtained by connecting three identical resistors in all possible ways.

1) Connect all resistors in series:

R1 = R + R + R = R * n = 3 * 6 = 18 ohms.

2) Connect all resistors in parallel:

1 / R1 = 1 / R + 1 / R + 1 / R;

1 / R1 = n / R;

R1 = R / n = 6/3 = 2 ohms.

3) First we connect two resistors in series, and then the third resistor – in parallel:

R1 = R + R = 2 * R = 2 * 6 = 12 ohms.

1 / R2 = 1 / R1 + 1 / R;

1 / R2 = (R1 + R) / (R1 * R);

R2 = R1 * R / (R1 + R) = 12 * 6 / (12 + 6) = 72/18 = 4 ohms.

4) We connect first two resistors in parallel, and then the third resistor – in series:

1 / R1 = 1 / R + 1 / R;

1 / R1 = 2 / R;

R1 = R / 2 = 6/2 = 3 ohms.

R2 = R1 + R = 3 + 6 = 9 ohms.

Answer: when connecting resistors in all possible ways, you can get resistance values ​​equal to 18 Ohms (first method), 2 Ohms (second method), 4 Ohms (third method) and 9 Ohms (fourth method).



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