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12 V with 4 Ω and 12 Ω: series or parallel
A 12 V supply is connected to two resistors, R₁ = 4 Ω and R₂ = 12 Ω. What is the current from the supply when they are connected in series, and when they are connected in parallel?
Answer
Series total resistance 16 Ω; series current 0.75 A; parallel total resistance 3 Ω; parallel current 4 A
Step-by-step
- 4 + 12 = 16Series resistances add: R = R₁ + R₂
- 12 ÷ 16 = 0.75Ohm's law I = U / R
- 1 ÷ (1/4 + 1/12) = 3Parallel resistances add reciprocally: 1/R = 1/R₁ + 1/R₂
- 12 ÷ 3 = 4Ohm's law I = U / R (main current)
Why it works
Series resistances add, parallel resistances combine as reciprocals, and the supply current is the voltage divided by the total resistance. The parallel combination always draws the larger current.
Common mistakes
- Forgetting to take the reciprocal when combining the parallel resistors.
- Dividing 12 V by a single resistor instead of by the total resistance.
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