Question

(1 point) Unknown resistor in voltage divider Suppose that a power supply is connected across two resistors R1 and R2 that are connected in series. The power supply voltage E, the voltage across the second resistor V2, and the first resistance R1 are all known, but R2 is not known. Find an expression for R2 in terms of E,R1,andV2

Answer 1

Answer:

R₂ = V₂R₁/(E + V₂)

Explanation:

By voltage divider, V₂ = ER₂/(R₁ + R₂)

So, cross-multiplying, we have

V₂(R₁ + R₂) = ER₂

expanding the bracket, we have

V₂R₁ + V₂R₂ = ER₂

collecting like terms, we have

V₂R₁ = ER₂ + V₂R₂

factorizing, we have

V₂R₁ = (E + V₂)R₂

dividing through by (E + V₂), we have

R₂ = V₂R₁/(E + V₂)