The combined resistance in two identical resistors, connected in series is 8 ohm. Their combined resistance in a parallel arrangement will be what? Reply soon
Sure! To find the combined resistance of two identical resistors connected in series, you need to add the individual resistances. In this case, the combined resistance is given as 8 ohms.
Let's assume the resistance of each identical resistor is R. So, when the two resistors are connected in series, the total resistance is equal to R + R, which is 2R.
Therefore, 2R = 8 ohms. We can solve for R by dividing both sides of the equation by 2:
2R / 2 = 8 ohms / 2
R = 4 ohms
Now that we know the resistance of each individual resistor is 4 ohms, we can determine the combined resistance in a parallel arrangement.
In a parallel arrangement, the formula to calculate the combined resistance is given by:
1/R_parallel = 1/R1 + 1/R2 + 1/R3 + ...
Since we have only two resistors in this case, we can simplify the formula as:
1/R_parallel = 1/R + 1/R
1/R_parallel = 1/4 + 1/4
1/R_parallel = 2/4
Simplifying further:
1/R_parallel = 1/2
To find the combined resistance in a parallel arrangement, we take the reciprocal of both sides:
R_parallel = 2 ohms
Therefore, the combined resistance in a parallel arrangement of two identical resistors, each having a resistance of 4 ohms, is 2 ohms.