Answer key: Series & Parallel Circuits Worksheet
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Goal: Compare series and parallel connections of two resistors: the equivalent resistance, the total current and how the current divides between the branches.
Completed results table
| Setting | Equivalent R | Total current | Current R₁ | Current R₂ |
|---|---|---|---|---|
| 100 Ω and 200 Ω, series | 300 Ω | 0.04 A | 0.04 A | 0.04 A |
| 100 Ω and 200 Ω, parallel | 66.667 Ω | 0.18 A | 0.12 A | 0.06 A |
| Equal (100 Ω, 100 Ω), series | 200 Ω | 0.06 A | 0.06 A | 0.06 A |
| Equal (100 Ω, 100 Ω), parallel | 50 Ω | 0.24 A | 0.12 A | 0.12 A |
| Unequal (50 Ω, 200 Ω), series | 250 Ω | 0.048 A | 0.048 A | 0.048 A |
| Unequal (50 Ω, 200 Ω), parallel | 40 Ω | 0.3 A | 0.24 A | 0.06 A |
Answers
In series, the current through R₁ and R₂ was always the same. Why?
A series circuit has only one path, so every charge that passes through R₁ must also pass through R₂. With 100 Ω and 200 Ω the current is 0.04 A everywhere.
How do you find the equivalent resistance in series and in parallel? Check your rules with the 100 Ω and 200 Ω rows.
In series the resistances add: 100 + 200 = 300 Ω. In parallel, 1/R = 1/100 + 1/200, so R = 66.67 Ω, which is smaller than either resistor.
Why does the parallel circuit draw more total current from the same 12 V supply?
Its equivalent resistance is lower (66.67 Ω instead of 300 Ω), so I = V ÷ R is larger: 0.18 A instead of 0.04 A. Each branch gets the full 12 V and adds another path for current.
In parallel with 100 Ω and 200 Ω, which branch carries more current? How do the branch currents add up?
The 100 Ω branch carries 0.12 A and the 200 Ω branch 0.06 A, twice as much through the smaller resistance. Together they make the total: 0.12 + 0.06 = 0.18 A.
Two equal 100 Ω resistors in parallel give what equivalent resistance? Explain the pattern.
50 Ω, half of one resistor. Two equal resistors in parallel give R ÷ 2, because the current has two identical paths.
Challenge: in the unequal series circuit (50 Ω and 200 Ω), what is the voltage across each resistor? Use V = IR.
The current is 0.048 A, so V₁ = 0.048 × 50 = 2.4 V and V₂ = 0.048 × 200 = 9.6 V. They add up to the 12 V supply, and the larger resistor takes the larger share.