Voltage equals current times resistance: V = I × R. Rearranged, current I = V ÷ R and resistance R = V ÷ I. A 12 V battery across a 4 Ω resistor drives 3 A of current.

How do you add resistors in series and in parallel?

In series, resistances simply add: 2 Ω + 2 Ω + 2 Ω = 6 Ω. In parallel, the reciprocals add: 1/R = 1/R₁ + 1/R₂ + … Two equal resistors in parallel give half of one, so two 4 Ω resistors make 2 Ω.

Why is parallel resistance smaller than any single resistor?

Each resistor in parallel gives the current another path, so more current can flow for the same voltage. More paths mean less total resistance, always below the smallest resistor in the group.

Free tool · OAR Mechanical Comprehension

Ohm’s law calculator

Two calculators for the circuit questions on the OAR: Ohm’s law (V = I × R) with power, and the total resistance of resistors in series and in parallel.

Ohm’s law

V = I × R · power P = V × I

Result

Answer: 3 A
Power: 36 W
Check: 12 V = 3 A × 4 Ω

Resistors in series and parallel

Series: R = R₁ + R₂ + … · Parallel: 1/R = 1/R₁ + 1/R₂ + …

Result

All in series: 11 Ω
All in parallel: 1 Ω

In parallel, 3 resistors give less resistance than the smallest one alone; in series they simply add.

How the calculations work

Ohm’s law: V = I × R, so I = V ÷ R and R = V ÷ I. Example: 12 V across 4 Ω gives 3 A (36 W).
Series: one path, so the resistances add. 6 Ω + 3 Ω + 2 Ω = 11 Ω.
Parallel: several paths, so the reciprocals add. 1/6 + 1/3 + 1/2 = 1, so the three resistors together are 1 Ω, less than the smallest one.

Shortcuts worth knowing

Two equal resistors in parallel: half of one. Three equal ones: a third.
Two different resistors in parallel: product ÷ sum, for example 6 × 3 ÷ (6 + 3) = 2 Ω.
In series the current is the same through every resistor; in parallel the voltage is the same across every branch.

Test yourself: an OAR-style question

Three resistors with values of 20 ohms, 2 ohms and 14 ohms are connected in series. What is the total resistance of the circuit?

33 ohms
42 ohms
39 ohms
36 ohms

Show answer

D. 36 ohms

Resistors in series simply add: 20 + 2 + 14 = 36 ohms.

Questions like this come up on the Mechanical Comprehension section of the OAR. The 2,604 questions in the app each come with a written explanation.

FAQ

What is Ohm’s law?: Voltage equals current times resistance: V = I × R. Rearranged, current I = V ÷ R and resistance R = V ÷ I. A 12 V battery across a 4 Ω resistor drives 3 A of current.
How do you add resistors in series and in parallel?: In series, resistances simply add: 2 Ω + 2 Ω + 2 Ω = 6 Ω. In parallel, the reciprocals add: 1/R = 1/R₁ + 1/R₂ + … Two equal resistors in parallel give half of one, so two 4 Ω resistors make 2 Ω.
Why is parallel resistance smaller than any single resistor?: Each resistor in parallel gives the current another path, so more current can flow for the same voltage. More paths mean less total resistance, always below the smallest resistor in the group.

Sources

Checked against these sources on October 24, 2026. Ideal components: wires with no resistance, resistors that obey Ohm’s law. For OAR preparation only; not affiliated with or endorsed by the U.S. Navy. Calculations run in your browser.