Question

When resistors R₁and R₂ are connected in a parallel electric circuit, the total resistance is 1 / ((1/R₁) + (1/R₂)). This fraction is equivalent to

a. R₁ + R₂
b. (R₁ + R₂) / R₁R₂
c. R₁/R₂ + R₂/R₁
d. R₁R₂ / R₁ + R₂

Answer 1

The parallel resistance equation simplifies to (R₁R₂) / (R₁ + R₂), so the answer is b. (R₁ + R₂) / R₁R₂.

Step-by-step explanation:

When resistors R₁ and R₂ are connected in a parallel circuit, the total resistance Rp is given by the formula 1 / ((1/R₁) + (1/R₂)). This expression for Rp can be simplified to the equivalent resistance of (R₁R₂) / (R₁ + R₂).

The correct option that represents this simplified form is b. (R₁ + R₂) / R₁R₂.

Let's examine the simplification step-by-step:

1. Take the reciprocal of the sum of reciprocals, 1 / ((1/R₁) + (1/R₂)).
2. Multiply both the numerator and denominator by R₁R₂ to get R₁R₂ / (R₁ + R₂).