3 Ω and 6 Ω in series and parallel

The power supply voltage is 12 V, and the two fixed resistors are 3 Ω and 6 Ω respectively. Find the main circuit current when they are connected in series and when they are connected in parallel.

Step-by-step

1. 3 + 6 = 9
   Series resistances add: R = R₁ + R₂
2. 12 ÷ 9 = 1.3333
   Ohm's law I = U / R
3. 1 ÷ (1/3 + 1/6) = 2
   Parallel resistances add reciprocally: 1/R = 1/R₁ + 1/R₂
4. 12 ÷ 2 = 6
   Ohm's law I = U / R (main current)

Why it works

The equivalent resistance calculation differs for series and parallel connections: in series, resistances are added directly; in parallel, the reciprocals of the resistances are added together, and then the reciprocal of that sum is taken. Since the power supply voltage is the same in both configurations, a smaller equivalent resistance results in a larger main circuit current. This is why the parallel current is always greater. After calculating, you can use this rule to self-check: if the parallel current turns out to be smaller, the equivalent resistance was definitely calculated incorrectly.

Common mistakes

• Calculating the parallel equivalent resistance as the sum of the two resistances, or calculating it as the product divided by the sum and then taking the reciprocal again.
• Swapping the currents for series and parallel connections, or only answering for one configuration.
• Using volts for voltage and ohms for resistance but forgetting that current is measured in amperes, not milliamperes.

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