Understanding U, I, P, and E in 48 V DC*
From Electricity to Mechanics: Linking Voltage, Current, Power, and Energy
The 48 V DC systems (direct current) are now ubiquitous in light electric vehicles, robots, and even automated agricultural machinery.
But to properly size a motor, a controller, and a battery, one must understand how the fundamental electrical quantities — voltage, current, power, and energy — interact and their link with mechanics (torque and speed).
1. Basic Electrical Quantities
Voltage – U
Unit: volt (V)
Voltage represents the 'electrical pressure' that pushes electrons in a circuit, like water pressure in a pipe.
In a 48 V system, this voltage is generally stable and defined by the battery or power supply.
The higher the voltage, the easier it is to transmit power with less current — a key advantage to limit losses and reduce cable size.
Current – I
Unit: ampere (A)
Current is the flow of electrons circulating in the circuit — comparable to the flow of water in a pipe.
It directly reflects the motor's workload: the higher the torque required, the more current the motor draws.
Current and Heating
Current is the main source of heating in conductors, windings, and connectors.
Joule losses are proportional to the square of the current:
This means that simply doubling the current quadruples the heat dissipated.
Example:
If a 0.05 Ω cable carries 20 A:
\(P_{losses}=20^2 × 0.05\) =20 WpBy doubling the current to 40 A:
\(P_{losses}=40^2×0.05\)=80 Wp
Hence the interest, at equal power, in increasing the voltage (U) to reduce the current (I):
Thus, a 1 kW motor will consume:
20.8 A at 48 V
41.6 A at 24 V
The higher the voltage, the less the cables heat up and the thinner and lighter they can be, while maintaining the same overall efficiency.
Power – P
Unit: watt (W)
Power is the flow of energy, that is, the rate at which the system consumes or provides energy.
Electrical Power
This is the power absorbed by the motor from the battery or power supply.
It expresses what is drawn in electrical energy at a given moment.
Mechanical Power
When the motor transforms this electrical energy into motion, it is referred to as mechanical power:
where:
- C or \(τ\) = motor torque (in N·m)
- \(ω\) = angular speed (in rad/s)
The two powers are linked by the motor efficiency \(η):
In practice, for a BLDC motor with 90% efficiency:
Example:
A 48 V motor consuming 25 A delivers
\(P_{elec}=48×25=1200W\)With an efficiency of 90%, the useful mechanical power is
\(1200×0.9=1080W\)
Energy – E
Unit: Wh or J
Energy corresponds to the total amount of work done over a given period:
A 48 V – 40 Ah battery stores:
This allows powering a 1 kW motor for about 2 hours at full power.
2. From the Electrical World to the Mechanical World
The BLDC motor acts as an energy converter:
Thus, knowing the voltage and current allows estimating the available torque and rotational speed, and hence the mechanical power delivered.
This direct link is at the heart of motor sizing: starting from the mechanical need (torque, speed) to deduce the required electrical power.
3. Practical Application: Estimating Need and Autonomy
Example 1 — Quick Calculation of Current from a Mechanical Need
Objective: provide 900 W mechanical power at 48 V with a motor efficiency of 90%.
Electrical Power Required
Example 2 — Estimating Battery Autonomy
Battery 48 V – 40 Ah → 1920 Wh.
If the average motor consumption is 800 W:
4. In Summary
| Quantity | Symbol | Unit | Main Role | Key Relationship | Note |
| Voltage | U | Volt (V) | Electrical force (pressure) | \(U=R×I\) | Set by the source (battery) |
| Current | I | Ampere (A) | Electron flow | \(P_{losses}= I^2 ×R\) | Causes heating (losses ∝ I²R) |
| Power | P | Watt (W) | Energy flow | \(P_{elec}=U×I\) \(P_{mech}=C×ω=τ×ω\) \(P_{mech}=P_{elec}×η\) | Directly links electricity and mechanics (consider efficiency) |
| Energy | E | Wh or J | Total amount of energy | \(E=P×t\) | Determines battery autonomy |
To remember
U pushes the current
I transports energy (and generates heat)
P = U × I expresses instantaneous power
E = P × t translates the duration of use
C × ω = P links electricity and mechanics
By mastering these relationships, one can efficiently size a 48 V BLDC motor, avoid overheating, choose the right cables, and estimate the autonomy of a complete electrical system.
*: The technical information presented in this article is provided for informational purposes only. It does not replace the official manuals of the manufacturers. Before any installation, handling, or use, please consult the product documentation and follow the safety instructions. Torque.works cannot be held responsible for inappropriate use or incorrect interpretation of the information provided.