Basic Electrical Quantities: Charge, Current, Voltage, and Power (BME 211)

The basic scientific unit for electricity is the charge, measured in Coulombs (C).
Charge is accumulated by counting charges (electrons or positive charges) and multiplying by the elementary charge:
- The elementary charge e ≈ 1.6 \times 10^{-19} \text{ C}.
- Therefore, a single electron carries e = 1.6 \times 10^{-19} \text{ C}.
- If you have N electrons, the total charge is Q = N e.
Example calculations:
- If you have 10 electrons, Q = 10 \times 1.6 \times 10^{-19} \text{ C} = 1.6 \times 10^{-18} \text{ C}.
In practice, labs use smaller charge units: picocoulombs (pC), nanocoulombs (nC), or microcoulombs (µC).
Charge is always a multiple of the elementary charge; you cannot create or destroy charge, only transfer it (conservation of charge).
The law of conservation of charge underpins circuit analysis and the behavior of currents and voltages in circuits.

The movement of charge through a circuit is called current.
Current is the first time derivative of charge:
- I = \frac{dQ}{dt}
Current is measured in amperes (A), where 1 A = 1 C/s.
Charge is a quantity; current is a rate (charge per unit time).
To find how much charge has passed over a time interval, integrate current:
- Q = \int I\, dt
Current direction conventions:
- Historically, positive current was defined to flow from the positive terminal to the negative terminal, which is opposite to the actual electron flow.
- The flow of electrons is opposite to the defined current direction.
- “Five amperes flowing in this direction” implies electrons move in the opposite direction.
To completely specify current, you must state both magnitude and direction; you can also use a current arrow to indicate direction.
In circuits, the magnitude is often written with a direction; for example, "minus five amps flowing downward" is equivalent to "five amps flowing upward".
Driving force for current is a difference in charge (electric potential) between two locations.

Voltage (electrical potential difference) is the energy required to move a unit charge between two locations.
- It is defined with reference to two points: voltage is always specified as V(X) relative to Y, i.e., V = dW/dQ between two points.
- If you reference the voltage to ground, you may omit the reference in some contexts; otherwise, specify the other reference point.
Formal expression for voltage:
- V = \frac{\Delta W}{\Delta Q}
- Equivalently, voltage is the energy per unit charge, i.e., the slope of the energy vs. charge relationship.
Energy perspective:
- Moving positive charge from a higher potential to a lower potential provides energy to the circuit element.
- Conversely, moving positive charge from a lower potential to a higher potential requires energy input, such as when charging a battery.
Note: Voltage alone does not produce power; power requires current to flow:
- Energy to move charge is supplied by a source (e.g., a battery) and leads to current and energy transfer.

Power is the rate at which energy is provided or used:
- P = VI
- Unit: Watts (W) = Joules per second (J/s).
Energy is the total work done or energy transferred over time:
- If power is constant, E = P t where E is in Joules and t is time in seconds.
Real-world energy units:
- Electric bills use kilowatt-hours (kWh). One kilowatt-hour equals
- 1\ \text{kWh} = 3.6\times 10^{6}\ \text{J}.
Important distinction:
- Power is a rate (energy per unit time); charge and current are related to how much charge moves and how fast it moves, while voltage is the energy per unit charge.
Conservation of energy in circuits:
- Energy is conserved; the energy supplied by sources (batteries, power supplies) is absorbed or dissipated by circuit elements.

Direct Current (DC):
- A current or voltage that remains constant with respect to time.
- Common DC source: a battery (e.g., a 9 V battery) maintains a nearly constant voltage until it discharges.
- In notation, DC current is often represented by a capital I (I = I(t) is DC if I is constant).
Alternating Current (AC):
- A current that varies sinusoidally with time.
- A common example is the wall outlet power, which typically varies sinusoidally with a frequency of 60 Hz (in many regions).
- In notation, AC current is written as i(t) (lowercase) to emphasize time variation.
Relationship between DC and AC terminology in circuit analysis:
- DC current/voltage: I (constant with time) or V (constant with time).
- AC current/voltage: i(t) and v(t), time-varying waveforms (often sinusoidal).
60 Hz example details:
- Frequency f = 60 Hz, so the signal oscillates 60 times per second.
- The period T = 1/f = 1/60 s.

The direction of current is a convention; the actual physical flow may be electrons moving opposite to the defined current direction.
For clarity, always specify both magnitude and direction (e.g., I = 5 A to the right).
Sign conventions are important for applying Kirchhoff’s laws and other circuit analysis techniques.

Conservations:
- Charge conservation: total charge is conserved; charge can be redistributed but not created or destroyed.
- Energy conservation: energy cannot be created or destroyed; it is transferred from sources to loads.
Practical implications:
- A circuit element that is not connected to a complete path cannot supply power (e.g., a floating 9 V battery with no load does not deliver power).
- The energy delivered by a source is distributed among circuit elements (resistors, capacitors, inductors, etc.) according to their characteristics.
Foundational connections:
- These basic units and concepts (charge, current, voltage, power) form the basis for later topics like resistance, capacitance, and inductance, as well as circuit analysis methods.

Charge and elementary charge:
- e \approx 1.6 \times 10^{-19} \text{ C}
- Q = N e for N electrons (or total elementary charges).
Charge and current relationships:
- I = \frac{dQ}{dt}
- Q = \int I \ dt
Voltage and energy per unit charge:
- V = \frac{\Delta W}{\Delta Q}
- W = V Q (for a fixed path/charge transfer)
Power and energy:
- P = VI
- E = P t
Units to remember:
- Charge: C (coulombs); common submultiples: pC, nC, µC
- Current: A (amperes) = C/s
- Voltage: V (volts) = J/C
- Power: W (watts) = J/s
- Energy: J (joules); common usage: kWh for consumer energy use
Special notes:
- A voltage must be specified with a reference point (two locations) unless referencing ground.
- A battery provides voltage; power only flows if a current path exists, i.e., there is current in the circuit.
Concepts you will use in later topics:
- Conservation laws (charge and energy) as foundational principles for circuit analysis.