Combine series resistance

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Series equivalent resistance equals the two supplied resistances added. Formula: a+b. Variable key: a = first resistance (Ω), b = second resistance (Ω)
• Distinct worked inputs and result: A distinct series model has 2 Ω and 6 Ω: equivalent resistance 2+6=8 Ω.
• Assessment case 1: Supplied case 1: first resistance (Ω)=3; second resistance (Ω)=5, using the explicitly named quantities. Series equivalent resistance equals the two supplied resistances added. What result follows?
• Assessment case 2: Supplied case 2: first resistance (Ω)=4; second resistance (Ω)=6, using the explicitly named quantities. Series equivalent resistance equals the two supplied resistances added. What result follows?
• Assessment case 3: Supplied case 3: first resistance (Ω)=8; second resistance (Ω)=12, using the explicitly named quantities. Series equivalent resistance equals the two supplied resistances added. What result follows?
• Assessment case 4: Supplied case 4: first resistance (Ω)=5; second resistance (Ω)=10, using the explicitly named quantities. Series equivalent resistance equals the two supplied resistances added. What result follows?
• Assessment case 5: Supplied case 5: first resistance (Ω)=7; second resistance (Ω)=9, using the explicitly named quantities. Series equivalent resistance equals the two supplied resistances added. What result follows?
• Assessment case 6: Supplied case 6: first resistance (Ω)=10; second resistance (Ω)=15, using the explicitly named quantities. Series equivalent resistance equals the two supplied resistances added. What result follows?

Learn the idea

In a simple series branch the same current passes through each resistor and their voltage drops add. Equivalent resistance is the sum; component power limits remain separate constraints.

Series equivalent resistance equals the two supplied resistances added. The formula in the supplied model is a+b. Variable key: a = first resistance (Ω), b = second resistance (Ω). Use this sum only for series connection. Series elements share current, not necessarily voltage.

A distinct series model has 2 Ω and 6 Ω: equivalent resistance 2+6=8 Ω. No physical circuit is needed. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with first resistance (Ω)=4; second resistance (Ω)=5. Expected result: 9 Ω. Explain what changes and keep this assumption: No physical circuit is needed.

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