In any electrical circuit, voltage is equal to the electrical potential difference between two points, defined mathematically as the product of current and resistance in a linear DC circuit, or the total work done per unit charge to move electrons between those points. Whether you are sizing a dropping resistor for a 5V logic pin or calculating feeder wire for a 240V subpanel, understanding the exact equations that dictate voltage is the difference between a circuit that works and one that melts down.
The Core Equations: What Voltage Is Equal To in DC and AC
Voltage is not a single, static concept; its governing equation changes depending on whether you are dealing with steady DC, alternating current, or reactive components like inductors and capacitors. Below is a data-dense reference table mapping out exactly what voltage is equal to across the most common domains you will encounter on the bench or jobsite.
| Domain / Component | Equation (Voltage is equal to...) | Variables Defined | Real-World Benchmark |
|---|---|---|---|
| DC Resistive (Ohm's Law) | V = I × R | I = Current (Amps), R = Resistance (Ohms) | 12V = 2A × 6Ω (Standard LED strip segment) |
| AC True Power | V = P / (I × PF) | P = Real Power (Watts), PF = Power Factor | 120V = 1440W / (15A × 0.80 PF) (Inductive motor load) |
| Inductive Kickback | V = L × (di/dt) | L = Inductance (Henrys), di/dt = Rate of current change | 50V = 0.1H × (5A / 0.01s) (Relay coil collapse) |
| Capacitive Charge | V = Q / C | Q = Charge (Coulombs), C = Capacitance (Farads) | 5V = 0.05C / 0.01F (Supercapacitor backup bank) |
| Kirchhoff's Voltage Law (KVL) | V_source = Σ V_drops | Sum of all voltage drops in a closed loop | 24V = 12V + 8V + 4V (Series resistor network) |
According to Georgia State University's HyperPhysics, these relationships form the bedrock of circuit analysis. Notice that in AC circuits, the power factor (PF) becomes critical; if you ignore PF and assume V = P / I for an inductive load like a compressor motor, your calculated voltage will be dangerously inaccurate.
Worked Example: Calculating Voltage Drop in a 120V Branch Circuit
To understand what voltage is equal to in a real installation, we have to look at Kirchhoff's Voltage Law in action. The voltage at your load is equal to the source voltage minus the voltage dropped across the wiring. Let's run a numeric example that dictates wire sizing.
The Scenario: You are wiring a dedicated 120V outlet for a 15A resistive space heater. The run from the panel to the outlet is 100 feet. You initially plan to use 14 AWG NM-B (standard copper wire).
The Math:
- Find Wire Resistance: Per NEC Chapter 9, Table 8, 14 AWG uncoated copper has a resistance of roughly 3.14 ohms per 1,000 feet at 75°C.
- Calculate Total Loop Length: Current must travel to the load and back. 100 ft out + 100 ft back = 200 feet total.
- Calculate Wire Resistance (R): (200 ft / 1000 ft) × 3.14 Ω = 0.628 Ω.
- Calculate Voltage Drop (V_drop): Using Ohm's Law (V = I × R), the drop is equal to 15A × 0.628 Ω = 9.42V.
- Calculate Load Voltage: The voltage at the heater is equal to 120V - 9.42V = 110.58V.
The Result: A 9.42V drop represents a 7.85% voltage drop. The NEC recommends a maximum of 3% for branch circuits and 5% for the entire feeder-plus-branch combined. At 110.58V, your heater will underperform, and the wire will run warm. The fix: Step up to 12 AWG wire (1.93 Ω/1000 ft). The new drop is 15A × 0.386 Ω = 5.79V (4.8%), which is much closer to acceptable limits, though 10 AWG would bring it perfectly under 3%. As Fluke's field guide on voltage drop notes, excessive drop doesn't just dim lights; it causes motors to draw higher amperage to compensate for low voltage, leading to premature burnout.
Where You Meet This in Practice: Wiring and Installations
Understanding what voltage is equal to changes how you approach three distinct areas of electrical and electronic work:
1. Home Wiring and Feeder Sizing
When sizing a subpanel feeder, the voltage at the subpanel bus bars is equal to the utility source minus the I×R drop of the feeder wires. If you are running a 60A subpanel 150 feet away using 6 AWG THHN, you must calculate the drop at the maximum continuous load (usually 80% of the breaker, so 48A). If the calculated voltage at the subpanel falls below 114V (on a 120V leg), your AFCI/GFCI breakers may nuisance-trip, and 240V appliances will run inefficiently.
2. DC Solar and Battery Banks
In a 12V nominal LiFePO4 or lead-acid system, the voltage is rarely equal to 12V. A resting lead-acid battery sits at 12.6V, while an alternator or MPPT charge controller pushes it to 14.4V during the absorption phase. If you are designing a low-voltage disconnect (LVD) for an inverter, you must program the cutoff based on the voltage under load (which sags due to internal battery resistance), not the resting open-circuit voltage.
3. PCB Trace Routing
On a printed circuit board, copper traces act as low-value resistors. If a 5V logic rail is routed through a 10-mil trace carrying 500mA, the voltage at the microcontroller's VCC pin is equal to 5V minus the trace drop. If the drop exceeds 0.3V, an ESP32 or STM32 may experience brownouts and trigger the internal watchdog timer, causing endless reboot loops.
Common Confusions: What Voltage Is NOT
Even experienced hobbyists trip over a few semantic and physical distinctions when discussing voltage.
- Voltage vs. Current: To use the standard water analogy exactly once: voltage is equal to the water pressure in the pipe, while current is the actual flow rate of the water (gallons per minute). You can have high voltage (pressure) with zero current (a closed valve/open circuit), but you cannot have current without a voltage difference to push it.
- Nominal vs. Actual Voltage: A '120V' outlet is a nominal label. According to ANSI C84.1 standards, the actual measured voltage is allowed to range from 114V to 126V (Range A). When troubleshooting, never assume the voltage is exactly equal to the nominal sticker value; always measure it.
- EMF vs. Potential Difference: Electromotive Force (EMF) is the energy provided by the source (battery/generator) per unit charge. Potential difference (voltage) is the energy used by the circuit components. In a perfect world, they are equal. In reality, the terminal voltage of a battery is equal to its EMF minus the drop across its own internal resistance.
FAQ: Voltage Calculation Edge Cases
Is voltage equal to zero in a short circuit?
The voltage across the short itself is theoretically equal to zero (since R = 0, V = I × 0). However, the voltage across the wiring and the power supply's internal resistance will be equal to the full source voltage, which is why the wires overheat and the breaker trips.
Why is the voltage equal to the source when a circuit is open?
When a switch is open, resistance is infinite, so current (I) is zero. According to Ohm's Law, the voltage drop across the wiring (V = 0 × R_wire) is zero. By Kirchhoff's Voltage Law, the remaining source voltage must appear entirely across the open switch terminals. This is why you can measure 120V across an open wall switch with a multimeter.
Does voltage change when I switch from series to parallel batteries?
Yes. In a series string, the total voltage is equal to the sum of the individual cell voltages (e.g., four 3.2V LiFePO4 cells in series equal 12.8V). In a parallel configuration, the total voltage is equal to the voltage of a single cell (3.2V), but the amp-hour capacity and maximum current delivery multiply.
