6 V with 2 Ω and 3 Ω: series vs parallel

A 6 V supply is connected to two resistors, R₁ = 2 Ω and R₂ = 3 Ω. What is the current in the circuit when they are connected in series, and when they are connected in parallel?

Step-by-step

1. 2 + 3 = 5
   Series resistances add: R = R₁ + R₂
2. 6 ÷ 5 = 1.2
   Ohm's law I = U / R
3. 1 ÷ (1/2 + 1/3) = 1.2
   Parallel resistances add reciprocally: 1/R = 1/R₁ + 1/R₂
4. 6 ÷ 1.2 = 5
   Ohm's law I = U / R (main current)

Why it works

In series the resistances add up, while in parallel the reciprocals add up and the total resistance is smaller than either one. The current then follows Ohm's law I = U / R.

Common mistakes

• Adding the two resistances when they are in parallel.
• Expecting the parallel total resistance to be larger than 3 Ω.

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