To solve the problem of finding the equivalent resistance for each circuit, we need to analyze each circuit step by step. Let's go through each one:
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Circuit 1:
- Resistors: \(60 \, \Omega\) and \(40 \, \Omega\) in series.
- Formula for resistors in series: \( R_{\text{eq}} = R_1 + R_2 \).
- Calculation:
\[
R_{\text{eq}} = 60 \, \Omega + 40 \, \Omega = 100 \, \Omega
\]
Equivalent Resistance: \( \boxed{100 \, \Omega} \)
---
Circuit 2:
- Resistors: \(60 \, \Omega\) and \(40 \, \Omega\) in parallel.
- Formula for resistors in parallel:
\[
\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2}
\]
- Calculation:
\[
\frac{1}{R_{\text{eq}}} = \frac{1}{60} + \frac{1}{40}
\]
Find a common denominator (120):
\[
\frac{1}{R_{\text{eq}}} = \frac{2}{120} + \frac{3}{120} = \frac{5}{120} = \frac{1}{24}
\]
Therefore:
\[
R_{\text{eq}} = 24 \, \Omega
\]
Equivalent Resistance: \( \boxed{24 \, \Omega} \)
---
Circuit 3:
- Resistors: \(40 \, \Omega\) and \(60 \, \Omega\) in series.
- Formula for resistors in series: \( R_{\text{eq}} = R_1 + R_2 \).
- Calculation:
\[
R_{\text{eq}} = 40 \, \Omega + 60 \, \Omega = 100 \, \Omega
\]
Equivalent Resistance: \( \boxed{100 \, \Omega} \)
---
Circuit 4:
- Resistors: \(40 \, \Omega\) and \(60 \, \Omega\) in parallel.
- Formula for resistors in parallel:
\[
\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2}
\]
- Calculation:
\[
\frac{1}{R_{\text{eq}}} = \frac{1}{40} + \frac{1}{60}
\]
Find a common denominator (120):
\[
\frac{1}{R_{\text{eq}}} = \frac{3}{120} + \frac{2}{120} = \frac{5}{120} = \frac{1}{24}
\]
Therefore:
\[
R_{\text{eq}} = 24 \, \Omega
\]
Equivalent Resistance: \( \boxed{24 \, \Omega} \)
---
Circuit 5:
- Resistors: \(20 \, \Omega\) and \(40 \, \Omega\) in series.
- Formula for resistors in series: \( R_{\text{eq}} = R_1 + R_2 \).
- Calculation:
\[
R_{\text{eq}} = 20 \, \Omega + 40 \, \Omega = 60 \, \Omega
\]
Equivalent Resistance: \( \boxed{60 \, \Omega} \)
---
Circuit 6:
- Resistors: \(60 \, \Omega\), \(40 \, \Omega\), and \(40 \, \Omega\) in series.
- Formula for resistors in series: \( R_{\text{eq}} = R_1 + R_2 + R_3 \).
- Calculation:
\[
R_{\text{eq}} = 60 \, \Omega + 40 \, \Omega + 40 \, \Omega = 140 \, \Omega
\]
Equivalent Resistance: \( \boxed{140 \, \Omega} \)
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Final Answers:
1. \( \boxed{100 \, \Omega} \)
2. \( \boxed{24 \, \Omega} \)
3. \( \boxed{100 \, \Omega} \)
4. \( \boxed{24 \, \Omega} \)
5. \( \boxed{60 \, \Omega} \)
6. \( \boxed{140 \, \Omega} \)
Parent Tip: Review the logic above to help your child master the concept of series parallel resistor worksheet.
