Question

Three resistors in series have an RT of 7 kΩ. If R3 is 2.2 times larger than R1 and 1.5 times larger than R2, what are the values of R1 , R2 , and R3 ? ANSWER IN DETAIL.....

Answer 1

Answer:

R₁ = 1.272 kΩ

R₂ = 1.628 kΩ

R₃ = 4.072 kΩ

Explanation:

If 3 resistors are connected in series, then their equivalent resistance will be the product of each resistance.

∴ R₁ + R₂ + R₃ = 7 kΩ

Given,

• R₃ = 2.2R₁ + R₁ = 3.2R₁

• R₃ = 1.5R₂ + R₂ = 2.5R₂

(R₃/3.2) + (R₃/2.5) + R₃ = 7

(2.5R₃ + 3.2R₃ + 8R₃)/8 = 7

R₃ = 56/13.75 = 4.072 kΩ

R₂ = 1.628 kΩ

R₁ = 1.272 kΩ

∴ ,

• R₁ = 1.272 kΩ
• R₂ = 1.628 kΩ
• R₃ = 4.072 kΩ