Scientific Notation and Metric Conversions

Scientific Notation

• A number is expressed in scientific notation as a product of a number between 1 and 10 and a power of ten.
• Example: 150,000 = 1.5 × 10^5; 0.00022 = 2.2 × 10^-4.

Multiples and Sub-multiples

• Engineers use multiples and sub-multiples to simplify numbers and avoid excessive zeros.
• Common prefixes and their multipliers include:
  • Tera (T): 10^12
  • Giga (G): 10^9
  • Mega (M): 10^6
  • Kilo (k): 10^3
  • None: 10^0
  • Centi (c): 10^-2
  • Milli (m): 10^-3
  • Micro (µ): 10^-6
  • Nano (n): 10^-9
  • Pico (p): 10^-12

Powers of Ten

• Powers of ten are expressed as exponents, indicating decimal point movement.
• For a positive exponent, move the decimal point right; for a negative exponent, move it left.

Metric Unit Conversions

• To convert larger units to smaller units, move the decimal point right.
• To convert smaller units to larger units, move the decimal point left.
• The number of decimal places moved corresponds to the difference in the powers of ten.

Examples of Unit Conversion

• Convert between milliampere (mA) and microampere (µA) requires a three-place movement.
• Example: 0.15 mA to µA = 150 µA (move three places right).
• Example: 4,500 µV to mV = 4.5 mV (move three places left).

Electric Current

• Electric current (I) is the rate of charge flow, measured in amperes (A).
• 1 ampere = 1 coulomb/second.
• Current can be direct (DC) or alternating (AC):
  • DC: constant flow of current over time.
  • AC: current that varies sinusoidally with time.

Relationship Between Charge and Current

• Charge (q) can be calculated using the number of electrons or protons.
• Example: Charge from 4,600 electrons is -7.369 × 10^-16 C.
• Charge transferred over time can be calculated from current and time.

Voltage and Energy

• Voltage represents the potential difference, calculated as energy per charge.
• Example: Moving a charge of 6 C requires a voltage drop of -5V for -30 J of energy.

Power

• Power (P) is the rate of energy expenditure, measured in watts (W).
• Instantaneous power can be calculated as the product of voltage and current.
• Positive power indicates energy delivery; negative power indicates energy absorption.

Elements in Circuits

• Active elements generate energy (e.g., batteries, generators).
• Passive elements do not generate energy (e.g., resistors, capacitors).
• Independent sources provide constant voltage or current; dependent sources are controlled by other circuit elements.

Types of Sources

• Independent Voltage Source: Maintains terminal voltage irrespective of current.
• Independent Current Source: Maintains specified current irrespective of voltage.
• Dependent sources respond to circuit conditions, categorized as voltage-controlled or current-controlled sources.