Electric Current and Direct-Current Circuits

Electric Current

Electric current is a fundamental concept in physics, describing the flow of electric charge through a conductor. It is essential for understanding how electrical devices and circuits operate.

• Definition: Electric current is the flow of electric charge from one place to another.

• SI Unit: The unit of electric current is the ampere (A), defined as one coulomb per second (C/s).

• Electric Circuit: A closed path through which charge can flow, returning to its starting point, is called an electric circuit.

• Electromotive Force (emf): The potential difference between the terminals of a battery when disconnected is called the emf. Despite its name, emf is an electric potential, not a force.

• Direction of Current: Conventional current flows from the positive terminal to the negative terminal, which is opposite to the actual motion of electrons.

• Electron Motion: Electrons move slowly along a wire, with most of their motion being random. The electric signal propagates much faster than the electrons themselves.

Resistance and Ohm’s Law

Resistance is a property of materials that opposes the flow of electric current. Ohm’s law relates voltage, current, and resistance in many conductors.

• Ohm’s Law:

• Resistance:

• Unit of Resistance: The unit is the ohm (Ω), defined as volts per ampere.

• Resistivity: The resistance of a wire depends on its material, length, and diameter. Resistivity is a material property affecting resistance.

• Classification: Materials are classified as conductors, semiconductors, and insulators based on their resistivity.

• Temperature Dependence: For most materials, resistance increases with temperature. For semiconductors, resistivity decreases with increasing temperature. Superconductors have zero resistivity below a critical temperature .

Energy and Power in Electric Circuits

When charge moves across a potential difference, its potential energy changes. The rate at which energy is transferred is called power.

• Work Done:

• Electrical Power:

• Power for Ohmic Materials:

• Unit of Power: The watt (W) is the SI unit.

• Energy Usage: Electric companies bill in kilowatt-hours (kWh), a unit of energy.

Resistors in Series and Parallel

Resistors can be combined in series or parallel to simplify circuit analysis.

• Series Connection: Resistors connected end to end. The current is the same through each resistor.

• Equivalent Resistance (Series):

• Parallel Connection: Resistors connected across the same potential difference. The voltage is the same across each resistor.

• Equivalent Resistance (Parallel):

• Complex Circuits: Start by combining series or parallel resistors to simplify the circuit.

Kirchhoff’s Rules

Kirchhoff’s rules are used to analyze complex circuits that cannot be simplified into series or parallel combinations.

• Junction Rule: The current entering a junction equals the current leaving it (conservation of charge).

• Loop Rule: The algebraic sum of potential differences around a closed loop is zero (conservation of energy).

• Solving Circuits: Use both rules to set up equations for unknown currents.

Circuits Containing Capacitors

Capacitors store electric charge and energy. They can be connected in series or parallel, similar to resistors.

• Parallel Capacitors: The potential difference across each is the same. Equivalent Capacitance:

• Series Capacitors: Each capacitor carries the same charge. Equivalent Capacitance:

• Capacitors in series combine like resistors in parallel, and vice versa.

RC Circuits

RC circuits contain resistors and capacitors. The charging and discharging of capacitors in these circuits follow exponential laws.

• Charging Equation:

• Time Constant:

• Current Behavior: The current decreases exponentially as the capacitor charges.

Ammeters and Voltmeters

Measurement devices are used to monitor current and voltage in circuits.

• Ammeter: Measures current; connected in series. Should have very low resistance.

• Voltmeter: Measures voltage; connected in parallel. Should have very high resistance.

Summary Table: Resistivity Classification

The following table summarizes the classification of materials based on their resistivity:

Summary Table: Series and Parallel Connections

Example: Calculating Equivalent Resistance

Suppose you have three resistors in series: , , . The equivalent resistance is:

Example: RC Circuit Charging

If a capacitor of is charged through a resistor of , the time constant is:

Example: Ammeter and Voltmeter Placement

• An ammeter is placed in series with the circuit element whose current is to be measured.

• A voltmeter is placed in parallel across the circuit element whose voltage is to be measured.

Additional info: The textbook cover is included to visually reinforce the source and context of the study notes, as these notes are based on the fifth edition of James S. Walker's Physics textbook.