Question

question
the total resistance in a circuit with two parallel resistors is 2 ohms and r₁ is 6 ohms.
using the equation for r_t in terms of r₁ and r₂, what is r₂?
r₂ is □ ohms.

Explanation:

Step1: Use the formula for parallel resistors

The formula for the total resistance \(R_T\) of two parallel resistors \(R_1\) and \(R_2\) is \(\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}\). Given \(R_T = 2\) ohms and \(R_1=6\) ohms. Substitute the values: \(\frac{1}{2}=\frac{1}{6}+\frac{1}{R_2}\).

Step2: Solve for \(\frac{1}{R_2}\)

\(\frac{1}{R_2}=\frac{1}{2}-\frac{1}{6}\). Find a common - denominator (6): \(\frac{1}{R_2}=\frac{3 - 1}{6}=\frac{2}{6}=\frac{1}{3}\).

Step3: Find \(R_2\)

Take the reciprocal of \(\frac{1}{R_2}\). So \(R_2 = 3\) ohms.

Answer:

3