Study Notes on Current Electricity

UNIT 16: CURRENT ELECTRICITY

STUDENT LEARNING OUTCOMES

• [SLO: P-10-E-20] Define and calculate electric current.

• [SLO: P-10-E-21] Explain electrical conduction.

• [SLO: P-10-E-22] State that current is measured in amps (amperes) and that the amp is given by coulomb per second (C/s).

• [SLO: P-10-E-23] Differentiate between direct current (d.c.) and alternating current (a.c.).

• [SLO: P-10-E-24] Differentiate between conventional and actual current.

• [SLO: P-10-E-25] Justify and illustrate the use of ammeters.

• [SLO: P-10-E-26] Define e.m.f. (electromotive force).

• [SLO: P-10-E-27] Define p.d. (potential difference).

• [SLO: P-10-E-28] State that e.m.f. and p.d. are measured in volts and that the volt is given by joule per coulomb (J/C).

• [SLO: P-10-E-29] Justify and illustrate the use of voltmeters.

• [SLO: P-10-E-32] Describe an experiment to determine resistance.

• [SLO: P-10-E-33] Define and calculate resistivity.

• [SLO: P-10-E-34] Define and apply Ohm's law.

• [SLO: P-10-E-35] Describe the effect of temperature increase on the resistance of a resistor.

• [SLO: P-10-E-36] Interpret current-voltage graphs.

16.1 ELECTRIC CURRENT

• Definition: Electric current is characterized as a stream of charged particles flowing through a conductive pathway (e.g., a wire). It plays a crucial role in powering electrical devices in households and gadgets.

• Nature of Electric Current:
    - Electric current arises from the movement of charged particles:
      - In metals: Flow of negatively charged electrons.
      - In particle accelerators: Flow of positively charged protons.
      - In gases and electrolytes: Flow of both positive and negative charges.

• Rate of Flow: The electric current can be defined by the time rate of flow of electric charges through a cross-sectional area:
    - Formula for electric current:
      $I = rac{Q}{ riangle t}$,
      where I is electric current, Q is charge, and Δt is time.
    - SI Unit: Ampere (A)
      - 1 Ampere is defined as when one coulomb of charge flows through a cross-section in one second. Mathematically:
      $1A = rac{1C}{1s}$

• Sub-multiples of Ampere:
    - $1 ext{ milliampere (mA)} = 10^{-3} ext{ A}$
    - $1 ext{ microampere (μA)} = 10^{-6} ext{ A}$

16.1.1 CONVENTIONAL FLOW OF CURRENT

• Initially, it was believed that electric current was due to the flow of positive charges. This assumption established the concept of conventional current, which is defined as the flow of positive charges from the positive terminal to the negative terminal of a battery.

• In practical applications, the direction of movement of negative charges can be treated as equivalent for conventional current, leading to understanding circuit behavior and analysis.

16.1.2 ELECTRICAL CONDUCTION IN METALS

• Characteristics of conduction in metals:
    - Valence electrons in metals are relatively free to move, similar to gas molecules in a container.

• Behavior without Battery: When metal (e.g., copper wire) is not powered, free electrons do not exhibit net movement; thus, no current flows.

• Behavior with Battery: When a battery is applied, free electrons start moving towards the positive terminal (attracted) and via the negative terminal (repelled), creating a drift of electrons that forms an electric current.

• Collisions: Electrons collide with one another and with lattice atoms, affecting the flow of current.

Example 16.1

• Battery Charging: If an electric car battery charges at a current of 10.0 A for 2 hours, the charge (Q) transferred:
    - Given: Current, $I = 10.0 A$; Time, $riangle t = 2 ext{ hr} = 7200 ext{ s}$
    - Required: Charge, $Q$
    - Using the formula:
      $Q = I imes riangle t$
      $Q = 10.0 imes 7200 = 72000 ext{ C}$
      - This can also be expressed as 20 Ah (Amp-hours).

16.2 ALTERNATING AND DIRECT CURRENT

• Types of Current:
    - Alternating Current (AC): Changes direction periodically.
    - Direct Current (DC): Flows in a single constant direction.

• Behavior in Circuit Elements: DC flows steadily, while AC periodically switches directions, influenced by the polarity of the voltage source.

• Danger of Electric Shock: AC at high voltage (>500 V) is more dangerous compared to DC due to its potential to cause continuous muscle contractions.

16.3 POTENTIAL DIFFERENCE

• Definition: The difference in electric potential between two points in a circuit due to connecting a conductor to a power source (e.g., a battery).

• Behavior: The positive terminal is at a higher potential, while the negative terminal is lower, allowing current flow as long as a potential difference exists.

• Mathematically:
      $ext{Potential Difference (V)} = rac{W}{Q}$,
      where W is work done and Q is charge.

• SI Unit: Volt (V) with the relation
    - One volt corresponds to one joule of work required to move one coulomb of charge.

16.4 EMF (ELECTROMOTIVE FORCE)

• Definition: The energy supplied by a source (e.g., a battery) to move charge in a circuit, termed emf.

• Mathematically:
      $ext{emf (E)} = rac{W}{Q}$

• Sources: Typical emf sources include batteries, solar panels, thermocouples, and generators, all converting one form of energy to electrical energy.

16.5 OHM'S LAW

• Statement: The law relates the current flowing through a conductor to the potential difference across it, under constant temperature conditions.

• Mathematically:
      $I ext{ is proportional to } V$, thus:
      $V = I imes R$
      where R is resistance.

• Types of Devices:
    - Ohmic devices: Follow Ohm's law (e.g., copper, silver).
    - Non-ohmic devices: Do not (e.g., filament bulbs, thermistors).

Limitations of Ohm's Law

• Applicable only for materials yielding a linear V-I graph (e.g., metallic conductors) and does not apply under extreme conditions.

Example 16.2

• Circuit Analysis: With a torch bulb using 2 cells of 1.5 V (series connection), total voltage is 3.0 V. If resistance is 20 ohms:
    - Use:
      $I = rac{V}{R} = rac{3.0 ext{ V}}{20 ext{ } ext{Ω}} = 0.15A = 150mA$

16.6 RESISTANCE

• Definition: The opposition to the flow of electric current. Formula:
    $R = rac{V}{I}$

• SI Unit: Ohm (Ω).

• Factors Affecting Resistance:
    - Length of Wire: Resistance increases with longer wires.
    - Cross-sectional Area: Resistance decreases with a larger area.
    - Temperature: Resistance of most conductors increases with temperature due to increased atomic vibrations.
    - Material: Different materials have different resistivities, affecting current flow.

Example 16.3

• Calculating Resistance: For a device connected to a 12V battery allowing 200mA current:
    - $R = rac{V}{I} = rac{12 ext{ V}}{0.2 ext{ A}} = 60 ext{Ω}$

16.7 RESISTIVITY

• Definition: Resistivity (ρ) is defined as the resistance of a conductor with a length of 1m and a cross-sectional area of 1m².

• Relation: $R = rac{ρL}{A}$, where R is resistance, L is length, and A is area.

• Unit of Resistivity: Ohm-meter (Ω·m).

Example 16.4

• Resistance of a Silver Wire: For a 1m silver wire (ρ = 1.6 x 10-8 Ω·m) and area A = 0.4 cm², calculate resistance. Transform area to m² (0.4 × 10^-4 m²) and apply formula:
    - $R = rac{ρL}{A}$ = 0.4 mΩ.

16.8 ELECTRICAL MEASURING INSTRUMENTS

• Ammeter:
    - Measures current (must be placed in series). Low resistance to minimize circuit disturbance.

• Voltmeter:
    - Measures potential difference (must be placed in parallel). High resistance to minimize impact on voltage measurement.

16.9 EXPERIMENT FOR DETERMINATION OF RESISTANCE

• An experimental setup usually includes an ammeter in series and a voltmeter in parallel with the unknown resistance. Use a variable resistor to observe changes in current and potential difference, recording values for resistance calculations.

SUMMARY

• Electric Current: Rate of flow of charges; measured in amperes.

• Potential Difference: Work done moving a charge through a field; measured in volts.

• Resistance: Opposition to current flow; dependent on material and physical dimensions.

• Ammeter and Voltmeter: Devices for measuring current and potential difference respectively.

EXERCISE & RESPONSES

• MCQs and Constructed Response Questions: Engage students in applying learned concepts through multiple-choice, short, and long response questions targeting key electrical principles and calculations.