To solve the problem of finding the total resistance for the resistors in series, let's break it down step by step.

Task 1: Calculate the total resistance of the resistors in series.

When resistors are in series, the total resistance ($R_{\text{total}}$) is simply the sum of all the resistances:

$R_{\text{total}} = R_1 + R_2 + R_3 + \ldots$

First Set of Resistors

• $R_1 = 1000 \, \Omega$
• $R_2 = 4700 \, \Omega$
• $R_3 = 22 \, \Omega$

$R_{\text{total}} = 1000 \, \Omega + 4700 \, \Omega + 22 \, \Omega = 5722 \, \Omega$

Second Set of Resistors

• $R_1 = 270 \, \Omega$
• $R_2 = 22000 \, \Omega$
• $R_3 = 15 \, \Omega$

$R_{\text{total}} = 270 \, \Omega + 22000 \, \Omega + 15 \, \Omega = 22285 \, \Omega$

Third Set of Resistors

• $R_1 = 3300 \, \Omega$
• $R_2 = 15000 \, \Omega$
• $R_3 = 47 \, \Omega$

$R_{\text{total}} = 3300 \, \Omega + 15000 \, \Omega + 47 \, \Omega = 18347 \, \Omega$

Final Results:

1. First Set: Total resistance = 5722 Ω
2. Second Set: Total resistance = 22285 Ω
3. Third Set: Total resistance = 18347 Ω

Would you like more details on the calculation or further explanations?

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Here are some related questions for further practice:

1. How do you calculate the total resistance for resistors in parallel?
2. What is the difference between resistors in series and resistors in parallel?
3. How does the total resistance change if another resistor is added in series?
4. What is the effect on current flow if the total resistance increases in a circuit?
5. How would you determine the total resistance if resistors were connected in a combination of series and parallel?

Tip: Always double-check your resistor values and units before performing calculations, as even a small mistake can lead to significant errors in the total resistance.