100 identical resistors of 2 Ohm each are connected in parallel. What is their total resistance? What is the total resistance

100 identical resistors of 2 Ohm each are connected in parallel. What is their total resistance? What is the total resistance of two parallel-connected 1 and 2 ohm resistors?

First task.

Given:

R = 2 Ohm is the resistance of the resistors;

n = 100 pieces – the number of resistors.

It is required to find R1 (Ohm) – the total resistance of the resistors.

Since, according to the condition of the problem, the resistors are connected in parallel with each other, then:

1 / R1 = 1 / R + 1 / R + ….. 1 / R;

1 / R1 = n / R;

R1 = R / n = 2/100 = 0.02 Ohm.

Answer: The total resistance of the resistors is 0.02 ohms.

Second task.

Given:

R1 = 1 Ohm – resistance of the first resistor;

R2 = 2 Ohm – the resistance of the second resistor.

It is required to determine the total resistance of the resistors R (Ohm).

Since, according to the condition of the task, the resistors are connected in parallel with each other, then:

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

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

R = R1 * R2 / (R1 + R2) = 1 * 2 / (1 + 2) = 2/3 = 0.7 ohms.

Answer: The total resistance of the resistors is 0.7 ohms.