Current, resistance, series and parallel
Answers are for parents and teachers.
1
A current of 40 mA flows for 5 minutes. Find the charge in coulombs.
I = 0.04 A and t = 5 × 60 = 300 s, so Q = 0.04 × 300 = 12 C.
2
A copper wire has ρ = 1.7 × 10⁻⁸ Ω·m, length 50 m and cross-section 2 mm². Find its resistance.
A = 2 × 10⁻⁶ m². R = (1.7 × 10⁻⁸ × 50) ÷ (2 × 10⁻⁶) = 0.425 Ω.
3
Resistors of 15 Ω and 25 Ω are in series with a third resistor across 60 V, and the current is 0.75 A. Find the third resistor and the drop across it.
Total R = 60 ÷ 0.75 = 80 Ω, so R₃ = 80 − 15 − 25 = 40 Ω. Its drop is 0.75 × 40 = 30 V. Check: 11.25 + 18.75 + 30 = 60 V.
4
Resistors of 3 Ω, 6 Ω and 2 Ω are in parallel across 12 V. Find the equivalent resistance, each branch current and the total current.
1 ÷ R = 1/3 + 1/6 + 1/2 = 2/6 + 1/6 + 3/6 = 6/6, so R = 1 Ω. Branches: 4 A, 2 A and 6 A. Total 12 A = 12 ÷ 1.
5
Explain in two sentences why the equivalent resistance of resistors in parallel is smaller than the smallest of them.
Each new branch gives the charge one more path at the same voltage, so more current flows than through the best branch alone. More current at the same voltage means a smaller equivalent resistance.