Key Concepts

Current $(I)$

• Measure of current describes the rate of flow of electrical charge in amperes or amps (coulombs per second).

  $$ 1A=1\frac{C}{s} $$

  • 1 coulomb of charge crosses a point in a circuit per second.

• Current is said to flow through a cross-section of a circuit, which can be measured along two points in a circuit.

  • By convention, a current is said to travel from a more positive charge to a more negative charge, thus this is used as a referenced current.
    • Actual direction of flow for electrons is the opposite direction, but this is ignored for simplicity.

• Note across two points, current flowing in the opposite direction along the same point will have the same magnitude but flow in opposite directions, thus the following relationship can be denoted:

  $$ I_{ab}=-I_{ba} $$

• Current can also describe the net charge through a section of a circuit.

  • We obtain a net charge as a function of $q(t)$ over time.

    $$ i(t)=\frac{q(t)}{dt} $$

  • To find the net charge, you integrate $i(t)$ to get $q(t)$

$$ q(t)=\int_{t_0}^{t}i(t)dt+q(t_0) $$

Voltage $(V)$

• Measure of voltage describes the amount of energy (work done) transferred per charge in volts (joules per second).

  $$ 1V=1\frac{J}{C} $$

  • 1 coulomb of charge delivers 1 joule of energy.

• Voltage is said to be applied across two points in a circuit to generate current, usually measured across a component.

  • ‘Direction’ of energy flow is determined by the direction of current.

• Components are usually assigned reference polarities to outline how energy is absorbed/generated.

  • If energy travels from the lower potential to a higher potential, it means that the component is generating energy (positive charge), presumably from stored chemical energy (battery).
  • If energy travels from the higher potential to a lower potential, it means that the component is absorbing energy (negative charge), thus that energy dissipates into other forms of energy (heat, light, mechanical, etc.).

• Note that across two points, voltage in opposite polarities hold the same magnitude, but are opposite directions, thus can be described as the following:

  $$ V_{ab}=-V_{ba} $$

Referencing Convention

• Note that the following diagram has current flowing into the positive polarity (higher potential) of the component. This is the Passive Reference Configuration.
  • This reference outlines positive reference voltage polarity and positive current direction of flow generally used in circuitry.
  • Positive voltage indicates the component absorbing energy; negative voltage indicates the component generating energy.
    • This can be dictated with current as well - if current enters the negative polarity, this indicates that the component is generating energy.

Power $(W)$

• Measure of power outlines the energy (joules) that is supplied or absorbed by a component in watts (joules/second).

  • 1 watt will measure 1 joule of energy generated/dissipated per second.

  $$ P=V \cdot I=\frac{\cancel C}{s} \times \frac{J}{\cancel C}=\frac{J}{s} $$

• Following the Passive Reference Configuration, an element with a positive voltage (absorbing energy) generates positive power.

  $$ p=vi $$

  • If an element has a negative voltage (generating energy) the component generates negative power.

  $$ p=-vi $$