⚡ Electric Current

It is a flow of electric charges in an electrical conductor. The electric charge can be either electrons or ions.
According to the International System of Units, electric current intensity is measured in Amperes (A).
Current is measured by a device called an Ammeter, connected in series in the circuit.
Electric current is a scalar physical quantity, and its direction is the direction of positive charge movement (opposite to electron movement).

⚡ In this simulation: Close the circuit and observe the movement of electric charges and how they lose energy in the resistor.

This simulation shows electron movement in a simple circuit from lower to higher potential. Note that the term "electric current" means the movement of positive charges from higher to lower potential.

📐 Current Density

It is the current flowing per unit area in a conducting wire at a given point.
Current density is denoted by the symbol j
It is a vector quantity pointing in the direction of positive charge movement (opposite to electron movement).

\[j = \frac{i}{A}\] measured in \[\frac{A}{m^2}\]

Drift Velocity: It is the directed velocity of electrons in an electrical circuit.
Any conducting wire contains electrons moving randomly at high speed. When a potential difference is applied, the electron motion becomes a directed random velocity called drift velocity, which is very slow on the order of \[𝜗_d = 10^{-4} \frac{m}{s}\]

We have a conductor with cross-sectional area (A) and an electric field is applied. Electrons move opposite the field with drift velocity (𝜗𝑑). During time (dt), they travel a distance \(𝜗𝑑 \cdot dt\).
Thus, the volume of electrons passing through the cross-section is \(A \cdot 𝜗𝑑 \cdot dt\), so the number of electrons in this volume is \(n \cdot A \cdot 𝜗𝑑 \cdot dt\).
Each electron has a charge (-e), so the charge flowing through this area is: \[dq = - e \cdot n \cdot A \cdot 𝜗𝑑 \cdot dt\]

Thus we obtain the current: \[i = \frac{dq}{dt} = - e \cdot n \cdot A \cdot 𝜗𝑑\]
And current density: \[j = \frac{i}{A} = - e \cdot n \cdot 𝜗𝑑\]

⚡ Ohm's Law

Ohm's Law is a fundamental principle in electricity, named after the German physicist "Georg Simon Ohm".
It states that the potential difference across a metallic conductor is directly proportional to the current flowing through it, at constant temperature.

The constant ratio between voltage and current is called electrical resistance. The resistance of a conductor is constant and does not change with voltage.
The equation can be expressed as: \[V = I \cdot R\]

Electrical Resistance: The opposition of a material to the flow of electric current. \[R = \frac{V}{I}\]

📌 In this simulation: Ohm studied the relationship between current intensity and potential difference across an ohmic resistor. Choose an ohmic resistor value and change the potential difference each time, observe what happens to the current, repeat the experiment with another resistor.

🔬 Resistivity and Resistance

Electrical Resistance: The opposition of a material to the flow of electric current.
\[R = \frac{\Delta V}{i}\] Unit: Ohm (Ω) = V/A.

Electrical Conductance: \[G = \frac{i}{\Delta V} = \frac{1}{R}\] Unit: Siemens (S = A/V = 1/Ω).

Resistivity (\(\rho\)): \[\rho = \frac{E}{J}\] Unit: Ω·m.
\[R = \rho \cdot \frac{L}{A}\]

📋 Resistivity and Temperature Coefficient of some conductors (at 20°C)

We know that: \[E = \frac{\Delta V}{L} \quad,\quad J = \frac{i}{A}\] \[\rho = \frac{E}{J} = \frac{\frac{\Delta V}{L}}{\frac{i}{A}} = \frac{\Delta V \cdot A}{i \cdot L} = \frac{R \cdot A}{L}\] \[\boxed{R = \rho \cdot \frac{L}{A}}\]

Temperature Effect: \[\rho_T = \rho_0 [1 + \alpha (T - T_0)] \quad,\quad R_T = R_0 [1 + \alpha (T - T_0)]\]

🔧 Factors Affecting Ohmic Resistance

In this simulation, we notice that the resistance changes with the length, cross-sectional area, and the type of material of the resistor.

🎨 Resistor Color Code

(4 bands) Reading resistors through color codes
Carbon resistors can have 4 to 6 bands. The first band represents tens, the second band represents units, the third band is the multiplier (power of 10), and the fourth band represents tolerance.

🔋 Electromotive Force (EMF) and Internal Resistance

A battery does work on electric charges, giving them electrical energy and pushing them through the circuit, hence called Electromotive Force (ε).
When measuring the potential difference across the battery terminals with an open circuit, the reading equals the emf.
When the circuit is closed, the terminal voltage decreases due to the battery's internal resistance (r).
\[V_{terminal} = \varepsilon - I \cdot r\]

In an open circuit: current \(I = 0\), so \(V_{terminal} = \varepsilon\).
In a closed circuit: current \(I = \frac{\varepsilon}{R + r}\), so \(V_{terminal} = \varepsilon - I \cdot r = \frac{\varepsilon \cdot R}{R + r}\).

In this simulation: Compare the voltmeter readings for the two circuits (open and closed). The closed circuit has a loss in the source voltage. The reason is the internal resistance (r) inside the battery, measured in ohms (Ω).

🔗 Series Connection

In series connection, the current flows in a single path and passes through all components of the circuit.
In series connection: the current is the same through all components, the source voltage divides across the resistors, and the equivalent resistance increases.

\[I_{total} = I_1 = I_2 = I_3\]
\[V_{total} = V_1 + V_2 + V_3\]
\[R_{eq} = R_1 + R_2 + R_3 = \frac{V_{total}}{I_{total}}\]

In this simulation: Three resistors in series. Measure the total current and the current through each resistor, and measure the total voltage and the voltage across each resistor. Record the results in the table.

🔗 Parallel Connection

In parallel connection, the current flows through multiple paths to complete its circuit.
In parallel connection: the current divides among the components according to their resistance, and the source voltage equals the voltage across each branch.

\[V_{total} = V_1 = V_2 = V_3\]
\[I_{total} = I_1 + I_2 + I_3\]
\[\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\]
\[R_{eq} = \left(\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\right)^{-1} = \frac{V_{total}}{I_{total}}\]

In this simulation: Three resistors in parallel. Measure the total current and the current through each resistor, and measure the total voltage and the voltage across each resistor. Record the results in the table.

🔧 Mixed (Compound) Circuits

Mixed circuits contain groups of resistors, some connected in series and others in parallel.
Steps to calculate the equivalent resistance of a mixed circuit: Identify which resistors are in series and which are in parallel, then calculate the equivalent resistance step by step.

🔋 Electric Power and Energy

When a potential difference is applied in a circuit, the electromotive force of the battery does work on the charges and gives them electrical energy. \[dU = dq \cdot \Delta V = I \cdot dt \cdot \Delta V\]
Electric power: It is the rate of energy dissipation, denoted by \(P\). \[P = \frac{dU}{dt} = I \cdot \Delta V\]
It is measured in Watts (W) in the SI system.
According to Ohm's Law \(R = \frac{\Delta V}{I}\), power can also be written as: \[P = I^2 \cdot R = \frac{\Delta V^2}{R}\]

Important Note: Electrical energy consumed is given by \(E = P \cdot t\), measured in Joules (J) or kilowatt-hours (kWh).

💡 Bulb Brightness

When we talk about bulb brightness, we need to look for electrical power. The greater the bulb's power, the brighter it shines. \[P = V \cdot I = I^2 \cdot R = \frac{V^2}{R}\]
Bulb brightness depends on the power consumed: the bulb that consumes more power shines brighter.
Important Rule: In a series circuit, current is constant, so the bulb with higher resistance consumes more power (\(P = I^2 R\)) and is brighter.
In a parallel circuit, voltage is constant, so the bulb with lower resistance consumes more power (\(P = V^2 / R\)) and is brighter.

🎬 Simulation 1: Bulb Brightness in Different Circuits

🎬 Simulation 2: Mixed Circuit with 4 Bulbs and Switches

This is a simulation of a mixed circuit with a power supply, four identical bulbs, and three switches. Open and close the switches to make predictions about voltages, currents, and bulb brightness (related to power dissipated as heat and light).