Current, Resistance, and Directed-Current Circuits (Chapter 19 Study Notes)

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Current, Resistance, and Directed-Current Circuits

Goals for Chapter 19

This chapter introduces the fundamental concepts of electric current, resistance, and direct-current (DC) circuits. It covers the application of Ohm's law, the calculation of energy and power in circuits, the combination of resistors, Kirchhoff's rules, measurement devices, and RC circuits.

Electric Current: Understanding the flow of charge in a conductor.
Resistance and Ohm's Law: Studying how materials resist current and the relationship between voltage, current, and resistance.
Electromotive Force (emf): Exploring sources of emf and their role in circuits.
Energy and Power: Calculating energy transfer and power in electric circuits.
Resistor Combinations: Comparing series and parallel arrangements.
Kirchhoff's Rules: Applying rules to analyze complex circuits.
Measurement Devices: Understanding voltmeters, ammeters, and multimeters.
RC Circuits: Combining resistors and capacitors in practical applications.

Electric Current

Definition and Direction

Electric current is the rate at which charge flows through a conductor. Conventional current is defined as the flow of positive charge, even though in metallic conductors, electrons (negative charges) are the actual charge carriers.

Current (): , where is the charge passing through a cross-section in time .
Unit: Ampere (A), where .
Direction: By convention, current flows in the direction positive charges would move.
Example: Calculating the number of electrons moving in a wire (see Example 19.1).

Resistance and Ohm's Law

Definition and Calculation

Resistance is a measure of how much a material opposes the flow of electric current. Ohm's law relates the voltage across a resistor to the current flowing through it and its resistance.

Ohm's Law: , where is voltage, is current, and is resistance.
Unit: Ohm (), where .
Commercial Resistors: Resistors are labeled with color codes to indicate their resistance value.

Resistor Color Code

Resistor values are determined using colored bands. Each color represents a digit and a multiplier.

Band Color	As #	As a multiplier
Black	0	1
Brown	1	10
Red	2	100
Orange	3	1,000
Yellow	4	10,000
Green	5	100,000
Blue	6	1,000,000
Violet	7	10,000,000
Gray	8	100,000,000
White	9	1,000,000,000

Tolerance Code	Tolerance
None	20%
Silver	10%
Gold	5%

Resistivity

Material Dependence

Resistivity () is a property of materials that quantifies how strongly they resist current. It varies with temperature and material type.

Formula: , where is length and is cross-sectional area.
Metals: Resistivity increases with temperature.
Superconductors: Resistivity drops to zero below a critical temperature .

Table: Resistivities at Room Temperature

Conductors		Insulators
Silver	1.47 × 10-8	Glass	1010 – 1014
Copper	1.72 × 10-8	Lucite	1013
Gold	2.44 × 10-8	Quartz (fused)	1016
Aluminum	2.82 × 10-8	Teflon	1024
Tungsten	5.51 × 10-8	Wood	1010 – 1014
Steel	20 × 10-8
Lead	22 × 10-8
Mercury	95 × 10-8
Nichrome alloy	100 × 10-8

Electromotive Force (emf)

Definition and Analogy

Electromotive force is the energy per unit charge supplied by a source such as a battery. It is analogous to the height difference in a waterfall, which drives water flow.

emf (): The potential difference provided by a source when no current is flowing.
Internal Resistance: Real sources have internal resistance, reducing the terminal voltage when current flows.
Formula:

Energy and Power in Electric Circuits

Calculations and Applications

Energy and power in circuits are determined by the current, voltage, and time. Power is the rate at which energy is transferred.

Power ():
Alternative Forms: or
Example: Calculating the voltage across the heart given resistance and current (see Example 19.4).

Circuit Diagrams and Symbols

Symbolic Representation

Circuit diagrams use standardized symbols to represent components such as resistors, batteries, and switches. This simplifies analysis and communication.

Conventional Current: Shown as the flow of positive charge.
Electron Flow: Actual charge carriers in metals are electrons, moving opposite to conventional current.

Series and Parallel Circuits

Connections and Calculations

Resistors can be connected in series (end-to-end) or parallel (side-by-side), affecting the total resistance and current distribution.

Series:
Parallel:
Example: Comparing circuits with different arrangements (see Examples 19.5–19.7).

Combinations of Series and Parallel Arrangements

Problem Solving Strategies

Complex circuits often require combining series and parallel rules to find equivalent resistance and analyze current flow.

Strategy: Reduce the circuit stepwise by combining resistors.
Example: See Example 19.9 and Figures 19.21, 19.22.

Kirchhoff's Rules

Analyzing Complex Circuits

Kirchhoff's rules allow analysis of circuits that cannot be simplified into series or parallel combinations.

Junction Rule: The sum of currents entering a junction equals the sum leaving it.
Loop Rule: The sum of potential differences around any closed loop is zero.
Application: Used for multi-loop circuits (see Figure 19.24).

Water Pipe Analogy

Understanding Circuit Behavior

The flow of electric current in a circuit can be compared to water flowing through pipes, aiding conceptual understanding of Kirchhoff's rules.

Junction Rule Analogy: Water flow into a junction equals flow out.
Loop Rule Analogy: Water pressure drops around a closed loop sum to zero.

Recharging Situations

Batteries and Jump-Starting

Rechargeable batteries and jump-starting involve complex circuit behavior, including current direction and energy transfer.

Example: Analyzing circuits during battery charging and jump-starting (see Examples 19.10, 19.11).

Devices to Make Measurements

Voltmeters, Ammeters, and Multimeters

Various devices are used to measure voltage, current, and resistance in circuits.

Voltmeter: Measures potential difference; connected in parallel.
Ammeter: Measures current; connected in series.
Multimeter: Combines functions for voltage, current, and resistance.
Galvanometer: Traditional device for detecting current.

Resistors and Capacitors Combine: RC Circuits

RC Devices and Applications

RC circuits combine resistors and capacitors, exhibiting time-dependent behavior such as charging and discharging.

Charging a Capacitor:
Discharging a Capacitor:
Time Constant ():
Example: Camera flash circuit stores charge for rapid discharge.

Additional info: These notes expand on the brief points in the slides, providing definitions, formulas, and examples for self-contained study.