Electrical quantities are expressed using the conventional electrical units (volt, ampere, ohm) and their prefixes. Prefixes are used when the amounts being measured are too big or small to be represented in a suitable way using only the basic units.
Fundamental Electrical Units:
The standard electrical units for voltage, current, and resistance are the volt (V), ampere (A), and ohm (Ω), respectively, according to the International System of Units (SI). These units serve as the foundation for all electrical measurements.
Measurement Scale: An Overview
Quantities that are very large or tiny are frequently used in electrical circuits and systems. The SI system uses prefixes like kilo- (k-), milli- (m-), etc., which function as multipliers or divisors of the basic units, to overcome this difficulty. These predefined units (milliampere, kilovolt, etc.) make it easy to represent these kinds of quantities.
Units Commonly Used in Electrical Calculations:
Some frequently used electrical units that can be found in calculations and component specifications are referenced in the following table.
| Electrical Quantity | Measuring Unit | Symbol | Formula |
| Voltage | Volt | V or E | Unit of Electrical Potential V = I × R |
| Current | Ampere | I or i | Unit of Electrical Current I = V ÷ R |
| Resistance | Ohm | R or Ω | Unit of DC Resistance R = V ÷ I |
| Conductance | Siemen | G or ℧ | Reciprocal of Resistance G = 1 ÷ R |
| Capacitance | Farad | C | Unit of Capacitance C = Q ÷ V |
| Charge | Coulomb | Q | Unit of Electrical Charge Q = C × V |
| Inductance | Henry | L or H | Unit of Inductance VL = -L(di/dt) |
| Power | Watts | W | Unit of Power P = V × I or I2 × R |
| Impedance | Ohm | Z | Unit of AC Resistance Z2 = R2 + X2 |
| Frequency | Hertz | Hz | Unit of Frequency ƒ = 1 ÷ T |
Standardized Prefixes for Electrical Units
Electrical engineering works with a very broad variety of values. For example, resistances range from millions of ohms (1,000,000 Ω) to a few hundredths of an ohm (0.01 Ω).
Prefixes are used as multiples or sub-multiples of the standard electrical units to prevent complicated statements with lots of zeros for the decimal placement. The common prefixes and the abbreviations for them are shown in the following table.
| Prefix | Symbol | Multiplier | Power of Ten |
| Tera | T | 1,000,000,000,000 | 1012 |
| Giga | G | 1,000,000,000 | 109 |
| Mega | M | 1,000,000 | 106 |
| kilo | k | 1,000 | 103 |
| none | none | 1 | 100 |
| centi | c | 1/100 | 10-2 |
| milli | m | 1/1,000 | 10-3 |
| micro | µ | 1/1,000,000 | 10-6 |
| nano | n | 1/1,000,000,000 | 10-9 |
| pico | p | 1/1,000,000,000,000 | 10-12 |
Examples of Prefixed Electrical Units:
Take into consideration the following instances to demonstrate how prefixes are used with electrical units:
- 1 kV (kilovolt): This signifies 1,000 volts, essentially a shorthand way of writing a large voltage value.
- 1 mA (milliampere): This represents one-thousandth of an ampere, a convenient way to express a small current value.
- 33 kΩ (kilohm): This denotes 33,000 ohms, a more concise way to represent a high resistance value.
- 220 µF (microfarad): This signifies 220 millionths of a farad, a compact way to express a very small capacitance value.
- 1 kW (kilowatt): This represents 1,000 watts, a common way to denote high power values.
- 1 MHz (megahertz): This signifies one million hertz, a standard way to express high frequencies.
As we notice, prefixes like 'micro-' (µ-),'milli-' (m-), 'kilo-' (k-), and so on act as divisors or multipliers that allow us represent electrical quantities effectively over a wide range of values.
Converting Between Prefixed Units:
Working with electrical quantities may need you to deal with values represented using several prefixes. The relative scale between the prefixes could be used to convert between these prefixed units.
For example, suppose we want to convert one megahertz (MHz) to one kilohertz (kHz). Prefixes indicate that 'mega-' denotes one million (1,000,000) and 'kilo-' denotes one thousand (1,000). Hence, compared to 1 kHz, 1 MHz is practically 1,000 times larger.
This knowledge enables us to carry out the conversion. Since kHz is smaller than MHz, we convert it by dividing by the 1,000 factor that separates 'mega-' from 'kilo-'. To put it another way, one mega-hertz (or 1 MHz divided by one kHz) equals 1,000 kHz.
For conversions between any prefixed unit, the concept of multiplication or division by the appropriate factor based on the prefixes can be used.
For example, to convert kilohertz (kHz) to megahertz (MHz) in MHz, divide the result by 1,000 (the difference between 'kilo-' and 'mega-'). The decimal point in the value can be moved three places to the left to get the same result without explicitly dividing. This is due to the fact that three places to the left on the decimal represent a division by 1,000 (1000 = 1.000).
On the other hand, one would have to multiply by 1,000 in order to convert from MHz to kHz. This may be accomplished by shifting the value's decimal point three places to the right.
Additional Electrical Units
Although the fundamental units of electrical measurements are the Volt (V), Ampere (A), Ohm (Ω), and so on, other units are also essential for describing certain electrical values and quantities. Here are a few instances:
- Watt-hour (Wh): This unit of measurement represents the cumulative use of electrical energy. For example, 100 Wh of energy would have been consumed by a light bulb that used 100 watts for an hour. To denote larger energy volumes, the prefixes mega- (MWh) and kilo- (kWh) are sometimes used with wh. 1,000 Wh is equal to one kWh, and 1,000,000 Wh is equal to one MWh.
- Decibel (dB): A tenth of a Bel (B) is used to describe power, voltage, or current gain. When describing the ratio of input to output signals in speaker systems, audio circuits, or amplifiers, the logarithmic unit (dB) is commonly employed.
When representing gain or loss (attenuation) in electrical signals, notably voltage, current, or power, the decibel (dB) unit is very helpful. The unit is logarithmic and is based on the Bel (B).
Think of an amplifier circuit as an example. Using the formula 20log10 (VOUT / VIN), we can describe the voltage gain (increase) as the dB ratio of the output voltage (VOUT) to the input voltage (VIN).
The magnitude of gain or loss is indicated by the resultant dB value. When the output voltage is higher than the input, amplification is indicated by a positive dB value (such as +20 dB). On the other hand, attenuation is represented by a negative dB number (such as -20 dB), which denotes that the output voltage is lower than the input.
When the output voltage equals the input voltage (unity gain), a dB value of 0 denotes no change.
Even though electrical measurements primarily use units like volts and ohms, comprehending electrical circuits sometimes requires knowledge of the following extra concepts:
- Phase Angle (θ): This term stands for the time difference between the voltage and current waveforms in a circuit with the same periodic time, expressed in degrees or radians. The phase angle can be "leading" (current comes before voltage) or "lagging" (voltage comes before current) depending on the circuit element.
- Angular frequency, represented by the symbol ω, is mostly utilized in AC circuits and denotes the phasor connection between several waveforms. The unit of rotation is radians per second, or rad/s. Half a cycle is 180 degrees, or π radians, while a full cycle is 360 degrees, or 2π radians.
- Time Constant (τ): When a step input is applied to an impedance circuit or a linear first-order system, the time constant (τ) indicates how long it will take the output to reach 63.7% of its final (maximum or lowest) value. In essence, it shows the response time of the circuit.
Our next course covers DC circuit theory, including Kirchhoff's Circuit Laws. Together with an understanding of Ohm's Law, these concepts will enable you to calculate voltages and currents in complicated DC circuits.
References: Units of Electricity