https://file.aiquickdraw.com/mathbot/file/1726408167535uu5n7std.jpg

Sain vastaukseksi 1/R_3=1/R_2 - 1/R_1 + 1/R  Onko se oikein?

The equation provided in the image is:

\[
\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]

You are tasked with solving for \( R_3 \).

### Let's solve for \( R_3 \) step by step:

Starting from:

\[
\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]

1. First, subtract \( \frac{1}{R_1} \) and \( \frac{1}{R_2} \) from both sides to isolate \( \frac{1}{R_3} \):

\[
\frac{1}{R_3} = \frac{1}{R} - \left( \frac{1}{R_1} + \frac{1}{R_2} \right)
\]

2. Combine the terms inside the parentheses:

\[
\frac{1}{R_3} = \frac{1}{R} - \frac{1}{R_1} - \frac{1}{R_2}
\]

This expression shows \( \frac{1}{R_3} \), which you were aiming to find.

---

### To answer your question:
The result you got, \( \frac{1}{R_3} = \frac{1}{R_2} - \frac{1}{R_1} + \frac{1}{R} \), is **incorrect** because the signs are not right. The correct result is:

\[
\frac{1}{R_3} = \frac{1}{R} - \frac{1}{R_1} - \frac{1}{R_2}
\]

Let me know if you would like a more detailed explanation.

---

Here are 5 related questions:
1. How do you compute the overall resistance \( R \) for three resistors in parallel?
2. What is the formula for combining more than three resistors in parallel?
3. How do you solve for \( R_2 \) instead of \( R_3 \) in this equation?
4. What would happen to \( R_3 \) if \( R_1 \) and \( R_2 \) were equal?
5. Can you use this method for resistors in series as well?

**Tip:** When solving for a variable, always carefully isolate the term and check the signs of each part after moving terms across the equals sign!

Sain vastaukseksi 1/R_3=1/R_2 - 1/R_1 + 1/R. Onko se oikein?

This problem covers the calculation of R3 in a parallel resistor circuit. Using the formula 1/R = 1/R1 + 1/R2 + 1/R3, learn how to isolate R3 step by step. Ideal for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation