Question

The four resistors in the figure have an equivalent resistance of 12 Q. The resistances are as follows: R₁ = 8.0 Q, R₂ = 6.0Q, and R₃ = 2.0Q. Calculate the value of Rₓ

Answer 1

To find the value of unknown resistor Rₓ, we can set up the equation for equivalent resistance and solve for Rₓ.

Step-by-step explanation:

To find the equivalent resistance of four resistors connected in series, we simply add up the individual resistances. In this case, the resistances are R₁=8.0Ω, R₂=6.0Ω, R₃=2.0Ω, and R₄=Rₓ (unknown).

1. R_eq = R₁ + R₂ + R₃ + R₄
2. R_eq = 8.0Ω + 6.0Ω + 2.0Ω + Rₓ
3. Given that the equivalent resistance is 12Ω, we can set up the equation:
4. 12Ω = 8.0Ω + 6.0Ω + 2.0Ω + Rₓ
5. Simplifying the equation, we get: Rₓ = 12.0Ω - 16.0Ω
6. Rₓ = -4.0Ω

Therefore, the value of Rₓ is -4.0Ω.