Current and Current Density

Definition and Measurement of Electric Current

Electric current is a fundamental concept in physics, describing the flow of electric charge through a conductor. It is measured as the amount of charge passing through a cross-sectional area per unit time.

• Electric Current (I): Defined mathematically as , where is the differential charge and is the differential time.

• Units: The SI unit of current is the ampere (A), where .

• Direction: By convention, current flows in the direction opposite to the flow of electrons in a wire.

• Potential Difference: Charge will flow as long as there is a potential difference across the conductor.

Example: If a current of 80.0 mA exists in a wire for 10.0 minutes, the total charge passing is . The number of electrons is electrons.

Current Density

Current density describes how much current flows per unit area of a conductor.

• Current Density (J): , where is the cross-sectional area.

• Microscopic Form: , where is the number density of charge carriers, is the charge of each carrier, and is the drift velocity.

• Vector Form:

Drift Speed of Charge Carriers

Random Motion and Drift Velocity

Electrons in a metal move randomly at high speeds (~ m/s), but without an electric field, their average velocity is zero (). When a potential difference is applied, an electric field is established, causing a net drift of electrons.

• Drift Velocity (): The average velocity of charge carriers due to an electric field, typically less than 1 mm/s.

• Current Relation: , where is the cross-sectional area.

Example: For a copper wire with , , and , .

Resistance and Resistivity

Definition and Calculation

Resistance quantifies how much a material opposes the flow of electric current. Resistivity is a material property that affects resistance.

• Resistance (R): , where is resistivity, is length, and is cross-sectional area.

• Resistivity (): A property of the material; low indicates a conductor, high indicates an insulator.

• Units: Resistance is measured in ohms (), where .

Resistor Symbols:

Resistor Color Code

Resistors are identified by colored bands representing digits, multipliers, and tolerance.

Example: A resistor with bands: red, black, orange, gold has .

Ohm's Law and Ohmic Materials

Ohm's Law

Ohm's law relates the voltage across a conductor to the current flowing through it and its resistance.

• Ohm's Law:

• Current Density Form: , where is conductivity.

• Ohmic Material: A material is ohmic if (linear relationship).

Example: Ohm's experiment shows a linear vs. plot for a resistor, confirming Ohm's law.

Non-Ohmic Example: Thyrite does not follow Ohm's law; its vs. plot is nonlinear.

Temperature Dependence of Resistivity

Resistivity and Temperature

The resistivity of most materials changes with temperature.

• Temperature Dependence: , where is the temperature coefficient.

• Superconductors: Materials with below a critical temperature .

Example: Mercury is a superconductor below ; above , resistance increases with temperature.

Calculation Example: Given at and at , .

Measurement Devices: Ammeters and Voltmeters

Ammeters

An ammeter measures current and is connected in series with the circuit element. It has low internal resistance to minimize its effect on the circuit.

• Series Connection: Ensures all current passes through the ammeter.

• Multiple Ammeters: Can measure current through different branches or total current from the EMF source.

Voltmeters

A voltmeter measures the potential difference across a circuit element and is connected in parallel. It has high internal resistance to minimize current draw.

• Parallel Connection: Measures voltage drop across the component.

Power and Resistive Dissipation

Energy Dissipation in Circuits

When current flows through a resistor, electrical energy is converted to thermal energy (Joule heating).

• Power Dissipation:

• Alternative Forms:

• For an ideal EMF source:

Example: For a resistor with and , , .

Summary Table

Additional info:

• Superconductors exhibit zero resistivity below a critical temperature, leading to phenomena such as magnetic levitation (Meissner effect).

• Experimental setups with ammeters and voltmeters can determine if a device is ohmic or non-ohmic by analyzing the vs. relationship.