Three 72-ohm resistors are being wired in parallel for a heating circuit. You need the combined resistance and total current draw at 240V before the circuit is assembled.
Parallel Resistance Calculator
Electrical
Shows current and power if provided
R_total = R ÷ N (identical resistors)
Example: 3 × 10Ω in parallel = 10÷3 = 3.33ΩTotal resistance is always less than the smallest individual resistor.
Reference: AS/NZS 3000 Wiring Rules
Results are estimates for planning purposes. Verify with current standards and a qualified professional.
1 What this calculator does
Calculates the combined resistance of identical resistors wired in parallel. For N equal resistors each with resistance R, the total is R/N. Optionally calculates total current draw at a given supply voltage.
2 Formula & professional reasoning
N equal resistors in parallel:
Total resistance = R / N
General parallel formula (mixed resistors):
1/Total = 1/R1 + 1/R2 + 1/R3 + ...
Total current at voltage V: I = V / Total resistance
Total power: P = V x I = V^2 / Total resistance
In a parallel circuit, each resistor provides an additional path for current. More paths means lower total resistance. For N identical resistors, the math simplifies cleanly to R/N. For mixed-value resistors, the reciprocal formula is needed. Parallel circuits are fundamental in electrical installation -- most building circuits are parallel connections at distribution boards.
3 Worked examples
⚠️ Illustrative example only — not clinical or professional instruction.
Basic
Three equal resistors in parallel
Given: Resistance: 72 Ohm each | Quantity: 3 | Voltage: 240V
Working:
Total resistance: 72 / 3 = 24 Ohm | Current: 240 / 24 = 10A | Power: 240 x 10 = 2,400WAnswer: Total resistance: 24 Ohm | Current: 10A | Power: 2,400W
💡 Three 72-ohm heating elements in parallel act as a single 24-ohm load drawing 10A. Each element draws 240/72 = 3.33A. Total = 3 x 3.33 = 10A -- confirms the calculation.
Standard
Two resistors in parallel -- spot-check series calculation
Given: R1: 100 Ohm | R2: 100 Ohm | N: 2
Working:
Total: 100 / 2 = 50 Ohm | Verify: 1/50 = 1/100 + 1/100 = 0.02 -- confirmedAnswer: Total resistance: 50 Ohm
💡 Two equal resistors in parallel always give exactly half the individual resistance. Four equal resistors in parallel give one quarter. Simple and useful quick check.
Advanced
Checking whether additional parallel loads overload a circuit
Given: Existing: 2 x 72 Ohm heaters = 36 Ohm total | Adding: third 72 Ohm heater | 240V circuit
Working:
New total: 72/3 = 24 Ohm | New current: 240/24 = 10A | Was: 240/36 = 6.67A | Increase: 3.33AAnswer: Current increases from 6.67A to 10A when third heater added
💡 If the circuit is protected by a 10A breaker, adding the third heater runs it at exactly the breaker rating -- any inrush could trip it. Recommend upgrading to a 16A circuit or reducing the load.
4 Sanity check
Parallel resistance is always less than the smallest individual resistor
Total parallel R < any individual R | Adding more parallel paths always reduces total resistance
Quick sanity check: if your answer is larger than any individual resistor, you made a calculation error.
Current through each parallel branch
Each branch carries: V / Individual branch R | Total current = sum of all branch currents
N equal resistors rule
N x R Ohm resistors in parallel = R/N Ohm total | Doubles the count halves the resistance
Practical electrical note
Real wiring has cable resistance and contact resistance that reduce the theoretical parallel benefit slightly
5 Common errors
| Error | Cause | Consequence | Fix |
|---|---|---|---|
| Adding resistances directly for a parallel circuit | Applying series formula to a parallel arrangement | Total resistance grossly overestimated -- current and protection sizing wrong | Parallel resistors are NOT added together. Use R/N for equal resistors or the reciprocal formula for mixed values. Series resistors ARE simply added: Total = R1 + R2 + R3. |
| Not checking total current against circuit breaker rating when adding loads | Calculating individual load currents without summing | Circuit overloaded -- breaker trips or, worse, cables overheat | Always calculate the total current from all parallel loads (or from V / total parallel resistance) and compare to the circuit breaker rating and cable rating. |
| Treating all building circuit loads as simple resistances | Using Ohm's Law without power factor correction for mixed loads | Total current underestimated for circuits with motor loads | For circuits with mixed resistive and inductive loads, calculate apparent power (VA) by dividing real power (W) by power factor, then calculate current from apparent power divided by voltage. |
| Confusing parallel and series wiring in the physical installation | Wiring components in series when parallel is intended (or vice versa) | Parallel wiring in series: loads severely underpowered | Series wiring in parallel: one failure takes out entire circuit | In parallel: all positive terminals connected together, all negative terminals connected together. In series: output of one connects to input of the next. Verify physically before energising. |
6 Reference & regulatory links
7 Professional workflow
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