Calculating Circuit Voltage Drop
When electrical current moves through a wire, it is pushed by electrical potential (voltage) and it needs to surpass a certain level of contrary pressure caused by the wire. The voltage drop is the amount of electrical potential (voltage) loss caused by the contrary pressure of the wire. If the current is alternating, such contrary pressure is called impedance. Impedance is a vector, or two-dimensional quantity, consisting of resistance and reactance (reaction of a built-up electric field to a change of current). If the current is direct, the contrary pressure is called resistance.
Excessive voltage drop in a circuit can cause lights to flicker or burn dimly, heaters to heat poorly, and motors to run hotter than normal and burn out. It is recommended that the voltage drop should be less than 5% under a fully loaded condition. This can be achieved by selecting the right wire, and by taking care in the use of extension cords and similar devices.
There are four major causes of voltage drop:
The first is the choice of material used for the wire. Silver, copper, gold, and aluminum are among the metals with the best electrical conductivity. Copper and aluminum are the most common materials used for wires due to their relatively low price compared with silver and gold. Copper is a better conductor than aluminum and will have less voltage drop than aluminum for a given length and wire size.
Wire size is another important factor in determining voltage drop. Larger wire sizes (those with a greater diameter) will have less voltage drop than smaller wire sizes of the same length. In American wire gauge, every 6-gauge decrease doubles the wire diameter, and every 3-gauge decrease doubles the wire cross sectional area. In the Metric Gauge scale, the gauge is 10 times the diameter in millimeters, so a 50 gauge metric wire would be 5 mm in diameter.
Still another critical factor in voltage drop is wire length. Shorter wires will have less voltage drop than longer wires for the same wire size. Voltage drop becomes important when the length of a run of wire or cable becomes very long. Usually this is not a problem in circuits within a house, but may become an issue when running wire to an outbuilding, well pump, etc.
Finally, the amount of current being carried can affect voltage drop levels; an increase in current through a wire results in an increased voltage drop. Current carrying capacity is often referred to as ampacity, which is the maximum number of electrons that can be pushed at one time – the word ampacity is short for ampere capacity.
The ampacity of a wire depends on a number of factors. The basic material from which the wire is made is, of course, an important limiting factor. If alternating current is being sent through the wire, the speed of alternation can affect ampacity. The temperature in which the wire is used can also affect ampacity.
Cables are often used in bundles, and when they are brought together, the total heat which they generate has an effect on ampacity and voltage drop. There are strict rules about bundling cables which must be followed for this reason.
Cable selection is guided by two main principles. First, the cable should be able to carry the current load imposed on it without overheating. It should be able to do this in the most extreme conditions of temperature it will encounter during its working life. Second, it should offer sufficiently sound earthing to (i) limit the voltage to which people are exposed to a safe level and (ii) allow the fault current to trip the fuse in a short time.
Example
Calculating Circuit Voltage Drop
The voltage drop in a circuit refers to the reduction in voltage in an electrical circuit as electric current flows through it. This occurs due to the resistance of the materials in the circuit, and it is an important factor in understanding how electrical systems work.
The general approach to calculating voltage drop includes:
- Identifying the resistance of the circuit or components involved.
- Knowing the current flowing through the circuit.
- Applying Ohm's Law to calculate the voltage drop.
Voltage Drop Formula
The general formula for calculating voltage drop is:
\[ V = I \times R \]Where:
- V is the voltage drop across the component (in volts, V).
- I is the current flowing through the component (in amperes, A).
- R is the resistance of the component (in ohms, Ω).
Example:
If a circuit carries a current of 3 A through a resistor with a resistance of 10 Ω, the voltage drop is:
- Step 1: Multiply the current by the resistance: \( V = I \times R = 3 \times 10 = 30 \, \text{V} \).
Voltage Drop in Series Circuits
In a series circuit, the total voltage drop is the sum of the voltage drops across each component. The same current flows through all components, but each component may have a different voltage drop based on its resistance.
Example:
If a circuit has two resistors in series, with resistances of 5 Ω and 10 Ω, and the current is 2 A, the voltage drop across each resistor is:
- For the 5 Ω resistor: \( V_1 = 2 \times 5 = 10 \, \text{V} \).
- For the 10 Ω resistor: \( V_2 = 2 \times 10 = 20 \, \text{V} \).
- Total voltage drop: \( 10 + 20 = 30 \, \text{V} \).
Voltage Drop in Parallel Circuits
In a parallel circuit, the voltage drop across each branch is the same. However, the current through each branch may vary based on the resistance of each branch.
Example:
If two resistors are connected in parallel, each with a resistance of 10 Ω, and the total current in the circuit is 5 A, the voltage drop across each resistor is:
- Since the resistors are in parallel, the voltage drop across both resistors is the same: \( V = I \times R = 5 \times 10 = 50 \, \text{V} \).
Real-life Applications of Voltage Drop
Calculating voltage drop is crucial for designing and troubleshooting electrical circuits, and it has many practical applications, such as:
- Ensuring electrical equipment operates within safe voltage limits.
- Optimizing power distribution systems.
- Preventing overheating in wires and components by calculating voltage loss.
Common Units of Voltage Drop
SI Unit: The standard unit of voltage drop is the volt (V).
Voltage drop can also be expressed as a percentage of the total voltage supplied to the circuit.
Common Operations with Voltage Drop
Series Circuit: In series circuits, the voltage drop increases with the resistance, and the sum of all individual drops equals the total voltage supplied.
Parallel Circuit: In parallel circuits, the voltage drop is the same across all branches, but the current divides based on the resistance.
Excessive Voltage Drop: Excessive voltage drop in a circuit can cause equipment to malfunction or overheat, so it’s important to minimize it during design.
| Problem Type | Description | Steps to Solve | Example |
|---|---|---|---|
| Calculating Voltage Drop from Current and Resistance | Finding the voltage drop when the current and resistance in a circuit are known. |
|
If a circuit carries a current of \( 3 \, \text{A} \) through a resistor of \( 10 \, \Omega \), the voltage drop is \( V = 3 \times 10 = 30 \, \text{V} \). |
| Calculating Voltage Drop in Series Circuit | Finding the total voltage drop in a series circuit with multiple resistors. |
|
If a circuit has resistors of \( 5 \, \Omega \) and \( 10 \, \Omega \) in series with a current of \( 2 \, \text{A} \), the voltage drop across each resistor is \( V_1 = 2 \times 5 = 10 \, \text{V} \) and \( V_2 = 2 \times 10 = 20 \, \text{V} \). The total voltage drop is \( 10 + 20 = 30 \, \text{V} \). |
| Calculating Voltage Drop in Parallel Circuit | Finding the voltage drop in a parallel circuit, where all branches have the same voltage drop. |
|
If two resistors of \( 10 \, \Omega \) each are connected in parallel with a total current of \( 5 \, \text{A} \), the voltage drop across each resistor is \( V = 5 \times 10 = 50 \, \text{V} \), which is the same for all branches. |
| Real-life Applications | Applying voltage drop calculations to practical electrical problems. |
|
If a home electrical circuit with a resistance of \( 20 \, \Omega \) carries a current of \( 4 \, \text{A} \), use the formula \( V = 4 \times 20 = 80 \, \text{V} \) to calculate the voltage drop across the wiring. |
