كيفية الحساب Equivalent المقاومة: Series & Parallel (R₁ + R₂)
Find equivalent resistance for series (Rₜ = R₁ + R₂) and parallel (1/Rₜ = 1/R₁ + 1/R₂) pairs. مثال محلولs, traps, and a free calculator.
What Equivalent المقاومة Asks
Real circuits often have more than one resistor. Equivalent resistance Rₜ is a single value that behaves like the whole combination — same total current from the battery or same voltage drop across the branch.
For two resistors the rules are: series Rₜ = R₁ + R₂, and parallel 1/Rₜ = 1/R₁ + 1/R₂. All values are in ohms (Ω).
If you already have R₁ and R₂, open the free series & parallel resistance calculator first, then return here for spotting series vs parallel and linking to Ohm's law.
Series vs Parallel
Trace the wire: if current must pass through R₁ then R₂ with no split, it is series. If the wire splits so each resistor has its own path between the same two points, it is parallel.
The الصيغةs
After You Find Rₜ
Use equivalent R in Ohm's law V = IR to find total current or voltage across the combination.
For power dissipation, try the electric power calculator with P = I²R or P = V²/R once you know I or V.
When two resistors divide a supply voltage (not the same as parallel), use the voltage divider calculator instead.
Units
الشغلed Examples
Example 1: series 100 Ω and 220 Ω
Rₜ = 100 + 220 = 320 Ω.
Example 2: parallel 100 Ω and 100 Ω
1/Rₜ = 1/100 + 1/100 = 2/100, so Rₜ = 50 Ω. Shortcut: equal pair → R/2.
Example 3: parallel 6 Ω and 3 Ω
1/Rₜ = 1/6 + 1/3 = 1/6 + 2/6 = 3/6. Rₜ = 2 Ω. Check: (6×3)/(6+3) = 18/9 = 2 Ω.
Example 4: 12 V across 320 Ω series pair
After Example 1, I = V/R = 12/320 = 0.0375 A = 37.5 mA total through both resistors.
أخطاء شائعة
Check It on the Calculator
Series & parallel resistance calculator.
Learn Rₜ for series and parallel pairs and confirm every circuit homework number on the calculator.