Question

When two resistors having resistances R1 ohms and R2 ohms are connected in parallel, their combined resistance R in ohms is R = R1*R2/R1+R2 . Show that (d²ᴿ)*(dᴿ)/(dR1²)*(dR2²) = (4R²)/ (R1 + R2)⁴

Answer 1

The equivalent resistance of the two resistors in parallel is (R₁R₂) / (R₁ + R₂).

How to calculate the equivalent resistance of two resistors?

The equivalent resistance of the two resistors in parallel is calculated by applying the following formula as shown below.

The given resistance in parallel

R₁ and R₂

The equivalent resistance of the resistors is;

1/R = 1/R₁ + 1/R₂

The LCM of R₁ and R₂ = R₁R₂

1/R = (R₂ + R₁)/R₁R₂

We will take the inverse of the two sides of the equation, to obtain the value of the equivalent resistance (R).

R = (R₁R₂) / (R₁ + R₂)

The equivalent resistance, R = (R₁R₂) / (R₁ + R₂).