Answer:
When R1 = 2.193, R2 = 3.894
When R1 = 3.894, R2 = 2.193
Explanation:
We are told that when R1 and R2 are connected in series, the voltage is 12.6 V and the current is 2.07 A.
Formula for resistance is;
R = V/I
R = 12.6/2.07
R = 6.087 ohms
Since R1 and R2 are connected in series.
Thus; R1 + R2 = 6.087 ohms
R1 = 6.087 - R2
We are also told that when they are connected in parallel, the current is 8.98 A.
Thus, R = 12/8.98
R = 1.403 ohms
Thus;
(1/R1) + (1/R2) = 1/1.403
Let's put 6.087 - R2 for R1;
(1/(6.087 - R2)) + (1/R2) = 1/1.403
Multiply through by 1.403R2(6.087 - R2) to get;
1.403R2 + 1.403(6.087 - R2) = R2(6.087 - R2)
Expanding gives;
1.403R2 + 8.54 - 1.403R2 = 6.087R2 - (R2)²
(R2)² - 6.087R2 + 8.54 = 0
Using quadratic formula, we have;
R2 = 2.193 ohms or 3.894 ohms
Thus,
R1 = 6.087 - 2.193 or R1 = 6.087 - 3.894
R1 = 3.894 or 2.193
When R1 = 2.193, R2 = 3.894
When R1 = 3.894, R2 = 2.193
