| Supply V | Branch resistances | Branch voltages | Branch currents | Equivalent R | Total current |
|---|---|---|---|---|---|
| 12 V | 6 Ω, 12 Ω, 24 Ω | 12 V each | 2 A, 1 A, 0.5 A | 3.4286 Ω | 3.5 A |
Parallel voltage rule
For an ideal parallel network, every branch sees the same voltage:
V1 = V2 = … = Vs
DC resistive branches
- Ik = Vs / Rk
- Pk = Vs2 / Rk
- 1/Req = Σ(1/Rk)
- Itotal = Σ Ik = Vs/Req
AC impedance branches
- Zk = Rk + jXk
- Yk = 1/Zk, and Ytotal = ΣYk
- Zeq = 1/Ytotal
- Ik = Vs/Zk, Itotal = Vs/Zeq
- P = V2R/(R2+X2), Q = V2X/(R2+X2)
- Select DC for resistors, or AC for impedance.
- Enter the supply voltage and choose its unit.
- Enter branch loads and add branches if needed.
- For AC, enter R and X for each branch.
- Press Calculate to view results above the form.
- Use CSV or PDF buttons to export the report.
1) What this calculator solves
This tool models a parallel network where loads share the same supply voltage. You enter one source voltage and several branch loads, then it reports branch currents, branch power, and totals. It also estimates an equivalent resistance (DC) or equivalent impedance (AC) for sizing.
2) Why voltage stays equal in parallel
Parallel branches connect to the same two nodes, so the potential difference is identical across every branch. If the source is 12 V, each branch ideally sees 12 V. Small real‑world drops happen from wiring resistance, loose terminals, or an undersized supply.
3) DC branch current and power numbers
In DC mode, the calculator uses Ohm’s law for each resistor: I = V/R. With 12 V and a 6 Ω branch, current is 2 A and power is 24 W. A 12 Ω branch draws 1 A and dissipates 12 W. Power rises quickly as resistance falls.
4) Equivalent resistance behavior with more branches
Adding branches lowers the equivalent resistance because conductances add. For 6 Ω, 12 Ω, and 24 Ω in parallel, 1/Req = 1/6 + 1/12 + 1/24 = 7/24, so Req ≈ 3.4286 Ω. Total current becomes 12/3.4286 ≈ 3.5 A.
5) AC impedance option and reactance sign
AC mode accepts R and X for each branch, where X>0 indicates inductive behavior and X<0 indicates capacitive behavior. The calculator sums admittances (1/Z) to get Zeq. It then reports P (watts), Q (var), apparent power S (VA), and power factor for each branch and the total.
6) Practical measurement checks and tolerance
If you type measured branch voltages, the calculator compares their average with the supply voltage. A typical classroom check is within about 1% for short leads and moderate currents. If the average is far lower than the supply, inspect lead resistance, connector heating, or a current‑limited adapter.
7) Exporting results for labs and design notes
After you calculate, you can export a CSV for spreadsheets or a printable PDF for lab reports. A helpful workflow is to record supply voltage, list branch loads, then paste the exported totals into a wiring note. Always confirm that fuse, conductor gauge, and source rating exceed the computed total current.
1) Do all branches always have the same voltage?
Ideally, yes. In a true parallel connection, every branch is across the same two nodes. Real wiring and supply limitations can cause small drops, especially at high current.
2) What happens if I leave a branch blank?
A blank branch is treated as an open circuit and ignored in totals. This lets you keep the same layout while testing different numbers without deleting rows.
3) What if a branch resistance is 0 Ω?
That represents a short. The calculator shows extremely large current and warns you. In real systems, a short can trip protection, overheat wiring, or damage the source.
4) How do I enter capacitive or inductive reactance?
Use a negative X value for capacitive reactance and a positive X value for inductive reactance. The sign affects current angle, reactive power, and overall power factor.
5) Why is total power not just V times total current in AC?
In AC, V×I gives apparent power (VA). Real power (W) depends on power factor. The calculator reports P, Q, and S so you can separate heating power from reactive exchange.
6) Can I mix kΩ and Ω in the same run?
Use one unit setting per run. If some values are in kΩ, switch the unit to kΩ and enter all branches consistently, or convert them before entering.