To isolate \( R_{eq} \) in the equation

\[
\frac{1}{R_{eq}} = \frac{1}{r_1} + \frac{1}{r_2},
\]

follow these steps:

1. Start with the given equation:
   \[
   \frac{1}{R_{eq}} = \frac{1}{r_1} + \frac{1}{r_2}
   \]

2. Find a common denominator on the right-hand side:
   \[
   \frac{1}{R_{eq}} = \frac{r_2 + r_1}{r_1 r_2}
   \]

3. Take the reciprocal of both sides to solve for \( R_{eq} \):
   \[
   R_{eq} = \frac{r_1 r_2}{r_1 + r_2}
   \]

So, the equivalent resistance \( R_{eq} \) is given by

\[
R_{eq} = \frac{r_1 r_2}{r_1 + r_2}.
\]

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How does the equivalent resistance \( R_{eq} \) change as \( r_1 \) and \( r_2 \) increase?
2. What is the physical meaning of \( R_{eq} \) in a parallel circuit?
3. How does this formula change if \( r_1 \) and \( r_2 \) are identical?
4. How would you extend this formula to three resistors in parallel?
5. What would happen to \( R_{eq} \) if one of the resistances \( r_1 \) or \( r_2 \) approaches infinity?

**Tip:** When resistors are connected in parallel, the equivalent resistance is always lower than the smallest individual resistor in the network.

Learn how to isolate the equivalent resistance formula \( \frac{1}{R_{eq}} = \frac{1}{r_1} + \frac{1}{r_2} \) in electrical circuits. Understand the steps involved in finding the equivalent resistance \( R_{eq} = \frac{r_1 r_2}{r_1 + r_2} \). Suitable for high school students studying electrical engineering and physics.

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