Know that electric current is related to the flow of charge

4.2.2 Electric Current

Objective

Understand that electric current is the rate at which electric charge flows through a circuit, and be able to use this definition in simple calculations.

Key Concepts

• Current (I) is the **rate of charge flow** past a point in a circuit.
• Current is a **scalar quantity** – only its magnitude (size) is required; it has no direction.
• **Conventional current direction** is defined as the direction a **positive** charge would move (from the positive terminal to the negative terminal of a source).
• In metallic conductors the actual charge carriers are electrons, which move **opposite** to the conventional direction.
• Two common types of current:
• Direct current (DC) – the direction of charge flow remains constant with time.
• Alternating current (AC) – the direction of charge flow reverses periodically, usually sinusoidally. The number of reversals per second is the **frequency**, measured in hertz (Hz).

Definition & Formula

The electric current I is defined as the amount of charge ΔQ that passes a given point in a time interval Δt:

$$ I = \frac{\Delta Q}{\Delta t} $$

Because one ampere equals one coulomb per second, the definition directly links the unit of current to the unit of charge:

1 A = 1 C s⁻¹

Units & Symbols

Rearranging the Formula (AO2 tip)

• To find the **charge transferred**: Q = I × t
• To find the **time taken**: t = Q / I

Worked Example (AO2)

Problem: A circuit transfers 6 C of charge in 3 s. What is the current?

Solution:

1. Write the definition: \(I = \dfrac{\Delta Q}{\Delta t}\)
2. Substitute the given values: \(I = \dfrac{6\ \text{C}}{3\ \text{s}} = 2\ \text{C s}^{-1}\)
3. Recognise that 1 C s⁻¹ = 1 A, so \(I = 2\ \text{A}\).

Reverse calculation tip: If the current were 2 A and the time 3 s, the charge transferred would be \(Q = I t = 2 \text{A} × 3 \text{s} = 6\ \text{C}\).

Conventional Current vs. Electron Flow

1. Conventional current: Imagines positive charges moving from the positive terminal to the negative terminal.
2. Electron flow: In metals, electrons (negative charge) move from the negative terminal to the positive terminal – opposite to the conventional direction.

Microscopic View – Extension Material (Not required for core assessment)

For deeper insight, current can also be expressed in terms of charge‑carrier properties:

$$ I = n\,A\,v_d\,q $$

• n – number of charge carriers per unit volume (m⁻³)
• A – cross‑sectional area of the conductor (m²)
• v_d – drift velocity of the carriers (m s⁻¹)
• q – charge of each carrier (C). For electrons, \(q = -e = -1.6\times10^{-19}\ \text{C}\).

This relationship helps explain why metals conduct electricity so well: the “free electrons” in the conduction band can drift under an applied electric field.

Measuring Current (AO3 – Experimental Skills)

• Connection: An ammeter must be placed **in series** with the component whose current is to be measured so that the same charge passes through the meter.
• Analogue ammeter: Uses a moving‑coil mechanism. Select a range just above the expected current; start with the highest range and step down until a clear, non‑over‑range reading is obtained.
• Digital ammeter: Shows the current numerically. Many have an auto‑range function, but manual range selection can give better resolution for small currents.
• Safety tip: Always switch off the circuit before inserting or removing an ammeter to avoid accidental short‑circuits or damage to the instrument.

Practical Implications

• High currents produce heating: \(P = I^{2}R\). Excess heat can damage components or cause fire hazards.
• Human safety: Currents as low as 0.01 A (10 mA) through the heart can be dangerous.

Suggested Diagram

Summary Checklist

• Current I is the rate of charge flow: \(I = \Delta Q / \Delta t\).
• 1 A = 1 C s⁻¹ – this links the definition directly to the unit.
• Current is a scalar quantity (magnitude only).
• Conventional current direction is opposite to the actual electron movement in metals.
• DC has a constant direction; AC reverses direction periodically, with a frequency measured in hertz (Hz).
• Measure current with an ammeter in series; choose the correct range and observe safety procedures.
• Large currents cause heating (\(P = I^{2}R\)) and can be hazardous.
• Extension: \(I = n A v_d q\) links macroscopic current to microscopic carrier properties (optional for core exams).