Three 2 ohm resistors are connected in parallel. Find the total resistance — Physics problems | PhysLabo
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Resistance of three resistors in parallel

Easy 10 grade Electricity / Electric Current

Three resistors of resistance $R = 2$ ohm each are connected in parallel. Find the total resistance of the combination.

Given
  • $R_1 = R_2 = R_3 = 2$ ohm
  • $R = ?$
Hints
Hint 1 / 2
In a parallel connection add the reciprocal values of the resistances.
Hint 2 / 2
For $n$ identical resistors the total resistance is $R/n$.
Solution

In a parallel connection the reciprocal resistances add up:

$$\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{3}{2}$$

$$R = \frac{2}{3} \approx 0.67 \text{ ohm}$$

Answer

$R = 2/3 \approx 0.67$ ohm