# Electric Current and Charge ## Electric Current - Electric current is defined as **the rate of flow of charge** - Measured in **amperes (A)**, commonly shortened to amps - Symbol for current is $I$

Electric current: $I = \frac{\Delta Q}{\Delta t}$, where $I$ is current (A), $\Delta Q$ is change in charge (C), and $\Delta t$ is time interval (s)

- The equation $I = \frac{\Delta Q}{\Delta t}$ can be rearranged to give $Q = I \times t$ - This shows that charge transferred is directly proportional to both current and time - For a constant current, plotting charge against time produces a straight line - The gradient of this line equals the current

- **Conventional current** flows from positive to negative terminals - This is a historical convention from before electrons were discovered - In reality, the actual charge carriers in metals (electrons) move from negative to positive - Despite this, we always use conventional current direction in circuit analysis - When two conductors with opposite charges are connected by a wire, charge flows between them - This flow of charge creates a current - The current continues until the potential difference between the conductors is zero - Current can be observed in many everyday situations - Domestic wiring systems carrying electricity to appliances - Electronic devices like smartphones and laptops - Industrial equipment and machinery ### Measuring Current - Current is measured using an **ammeter** - Ammeters must always be connected **in series** with the component being measured - This ensures all the current flowing through the component also flows through the ammeter - In exam questions, assume the ammeter's resistance is negligible ### Worked Example: Determining Current **Question:** A charge of 12 C passes through a wire in 4.0 s. Calculate the current in the wire. **Answer:** Step 1: Write the equation relating current, charge and time $$I = \frac{\Delta Q}{\Delta t}$$ Step 2: Substitute values $$I = \frac{12}{4.0} = 3.0 \text{ A}$$ --- ## Electric Charge - Charge is a fundamental property of certain particles - **Positive charge** (+): carried by protons - **Negative charge** (−): carried by electrons - **Neutral charge**: neutrons have no net charge - Atoms are electrically neutral overall - Equal numbers of protons and electrons - Their charges cancel out to give zero net charge - The atomic nucleus contains protons and neutrons - Since neutrons are uncharged, the nucleus has a positive charge - This positive charge attracts the negatively charged electrons - In physics, charge is represented by the symbol $Q$ or $q$ ### The Coulomb

The coulomb (C) is the unit of electric charge, defined as the charge passing a point when a current of 1 A flows for 1 s: 1 C = 1 A s

- The coulomb quantifies the amount of electric charge - Named after French physicist Charles-Augustin de Coulomb - In SI base units: $1 \text{ C} = 1 \text{ A s}$ ### Quantisation of Charge - Electric charge is **quantised** - This means charge exists in discrete, indivisible packets - You cannot have a fraction of the smallest charge unit - The smallest unit of charge is the **elementary charge**, $e = 1.60 \times 10^{-19}$ C - All charges are integer multiples of this value - An electron has charge $-e = -1.60 \times 10^{-19}$ C - A proton has charge $+e = +1.60 \times 10^{-19}$ C

The proton and electron have the same magnitude of charge but opposite signs

- **Magnitude** refers to the size of the charge, ignoring whether it's positive or negative - For example, both $+3e$ and $-3e$ have magnitude $3e$ - The net charge on any particle or object is always a multiple of $e$ - An ion with charge $+2e$ has lost two electrons - An ion with charge $-3e$ has gained three electrons ### Worked Example: Calculating Charge from Elementary Charge **Question:** Calculate the total charge on a particle that has lost 5 electrons. Give your answer in coulombs. **Answer:** Step 1: Determine the charge lost - Each electron carries charge $-e = -1.60 \times 10^{-19}$ C - Losing 5 electrons means losing $5 \times (-1.60 \times 10^{-19})$ C of charge Step 2: Calculate the net charge - If the particle was initially neutral, losing negative charge makes it positive - Net charge $= +5e = +5 \times (1.60 \times 10^{-19})$ $$Q = +8.0 \times 10^{-19} \text{ C}$$

Although charge can be positive or negative, current is always expressed as a positive value in calculations

### Key Relationships | Quantity | Symbol | Unit | Equation | |----------|--------|------|----------| | Current | $I$ | ampere (A) | $I = \frac{\Delta Q}{\Delta t}$ | | Charge | $Q$ | coulomb (C) | $Q = I \times t$ | | Elementary charge | $e$ | coulomb (C) | $e = 1.60 \times 10^{-19}$ C | ### Practical Example: Phone Charging - When charging a mobile phone with a 2 A charger for 30 minutes: - Time in seconds: $t = 30 \times 60 = 1800$ s - Charge transferred: $Q = I \times t = 2 \times 1800 = 3600$ C - Number of electrons: $n = \frac{Q}{e} = \frac{3600}{1.60 \times 10^{-19}} \approx 2.25 \times 10^{22}$ electrons