Electromagnetism
Resistors Calculator
Calculate total resistance for series or parallel combinations. Enter any number of resistors separated by commas.
Total Resistance
Series: R = ΣRn | Parallel: 1/R = Σ(1/Rn)
Current (I = V/R)
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A
Power (P = VI)
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W
Step-by-Step Solution
Series and Parallel Resistors
Resistors are combined in circuits to achieve desired resistance values. In series, resistances simply add. In parallel, the reciprocal of the total equals the sum of reciprocals. Understanding both configurations is essential for circuit analysis, from household wiring to microchip design.
Series: R = R₁+R₂+... | Parallel: 1/R = 1/R₁+1/R₂+...
R = total resistance (Ω) | Each Rn = individual resistor value (Ω)
💡 In parallel circuits, the total resistance is always less than the smallest individual resistor. Adding more parallel paths gives electrons more routes, reducing overall resistance.
Real-World Applications
House Wiring
Household appliances are wired in parallel so each device gets full mains voltage and can be switched independently.
Voltage Dividers
Series resistors split a voltage proportionally. Used in sensor circuits and audio equipment tone controls.
Electronics
Resistors control LED brightness, set op-amp gain and define bias points in transistor amplifiers.
Battery Packs
Battery cells in series add voltages; cells in parallel add current capacity. Resistors model internal resistance.
Frequently Asked Questions
Why is parallel resistance always less than the smallest?
In parallel, each resistor provides an additional current path. More paths = less total resistance. Mathematically, 1/R_total = 1/R1 + 1/R2 + ... means R_total is always smaller than any single R.
How do I combine series and parallel groups?
Work from the inside out. First simplify parallel groups to their equivalent single resistor, then add series resistors. Repeat until you have one total resistance.
What happens if one resistor in a parallel circuit fails open?
If one branch opens (breaks), current simply stops flowing through that branch. The other branches continue working normally. This is why household appliances work independently.