Electrical Engineering: Scientific Notation & Prefixes

Scientific Notation

• Scientific notation expresses numbers as a product of a number (1 to 10) and a power of ten.
• Example: 150,000 is 1.5 × 10^5, and 0.00022 is 2.2 × 10^-4.

Multiples and Sub-multiples

• Electrical engineering involves a wide range of values where standard units can be expressed in simpler forms.
• Example of resistance values can range from less than 0.01Ω to more than 1,000,000Ω.
• Utilizing multiples and sub-multiples helps avoid excessive zeros in numeric representations.

Prefixes and their Multipliers

• Tera (T): 1 × 10^12 (1,000,000,000,000)
• Giga (G): 1 × 10^9 (1,000,000,000)
• Mega (M): 1 × 10^6 (1,000,000)
• Kilo (k): 1 × 10^3 (1,000)
• None: 1 × 10^0 (1)
• Centi (c): 1 × 10^-2 (1/100)
• Milli (m): 1 × 10^-3 (1/1,000)
• Micro (µ): 1 × 10^-6 (1/1,000,000)
• Nano (n): 1 × 10^-9 (1/1,000,000,000)
• Pico (p): 1 × 10^-12 (1/1,000,000,000,000)

Powers of Ten

• Powers of ten are expressed as exponents (10^x), indicating decimal point movement.
• Positive exponents move the decimal right; negative exponents move it left.
• Example: 10^4 requires a right move of four places; 10^-4 requires a left move of four places.

Engineering Notation

• Engineering notation allows one to three digits to the left of the decimal; exponents must be multiples of three.
• Example: 33,000 is 33 × 10^3 in engineering notation, compared to 3.3 × 10^4 in scientific notation.

Metric Unit Conversions

• Convert larger units to smaller units by moving the decimal point right; vice versa for smaller to larger.
• Calculate the number of decimal places to move by finding the difference in the powers of ten.
• Example: Converting from milliamperes (mA) to microamperes (µA) involves three places right due to a three-place difference.

Power and Energy in Circuits

• Power (P) is defined as the rate of energy transfer, measured in watts (W).
• Law of Conservation of Energy states that the total power in a circuit at any instant must equal zero.
• Energy is measured in joules (J), with electric utilities often expressing it in watt-hours (Wh).

Passive and Active Components

• Active elements generate energy; passive elements do not.
• Passive components: resistors, capacitors, inductors.
• Active components: generators, batteries, operational amplifiers, capable of delivering power.
• Independent sources maintain constant voltage/current regardless of circuit conditions.

Dependent Sources

• Dependent sources are influenced by other circuit elements, represented by diamond-shaped symbols.
• Types include voltage-controlled and current-controlled sources.

Calculations and Examples

• Calculate power using the formula P = VI (voltage times current).
• Example: 100-watt light bulb calculation based on usage over time.

Current and Voltage

• Current direction influences power sign; adheres to Passive Sign Convention.
• Positive power indicates power absorption; negative indicates power supply by an element.