Study Notes on Current Electricity

Chapter 22: Current Electricity

22.1 CURRENT AND CIRCUITS

Producing Electric Current

• When two conducting spheres at different potentials touch, charges flow from the higher potential to the lower potential until equilibrium is reached.

• Electric Current Definition: The flow of charged particles. In conductors, this is typically the movement of negatively charged electrons or positively charged ions, which results from a potential difference (voltage).

• For the flow to continue, a potential difference must be maintained. This can be achieved by a charge pump (e.g., battery, generator).

• Charge Pumping: Charge pumps include batteries (convert chemical energy to electric energy), photovoltaic cells (convert light energy), and generators (convert kinetic energy).

Visual Representation

• Figure 22-1 shows charge flow between conductors at different potentials, indicating how the flow stops when equilibrium is achieved. The flow can be maintained by an external energy source.

Electric Circuits

• An electric circuit is a closed loop through which charged particles flow to enable current.

• It includes a charge pump (increases potential energy) and a load (decreases potential energy).

• Examples of energy conversion devices include motors (electric energy to kinetic), lamps (electric energy to light), and heaters (electric energy to thermal energy).

• Energy Change in Circuits: The potential energy change of charges ($qV$) transforms into other energy forms across different circuit components.

Charge Conservation

• Charge is conserved in circuits. If one coulomb flows through a generator, the same amount flows through a load.

• Example: If the potential difference is 120 V, the generator does 120 joules of work on each coulomb.

Rates of Charge Flow and Energy Transfer

• Power Definition: Power ($P$) measures energy transfer rate. If energy ($E$) is transferred at rate $1 ext{ J/s}$, power equals $1 ext{ W}$.

• The flow of electrical charge is measured in amperes (A), where $1 ext{ A} = 1 ext{ C/s}$ (coulomb per second).

• Electric Current Equation: The equation for electric power is given by $P = IV$ (power = potential difference × current).

Example Problem: Electric Power

1. Problem: A 6-V battery delivers 0.5 A to a motor.

   • Find power consumed by motor:

     • $P = VI = (6 ext{ V})(0.5 ext{ A}) = 3 ext{ W}$

   • Calculate energy delivered in 5 min:

     • $E = Pt = (3 ext{ W})(300 ext{ s}) = 900 ext{ J}$

Resistance and Ohm's Law

• Resistance Definition: Resistance ($R$) is the ratio of potential difference ($V$) to current ($I$): $R = rac{V}{I}$.

• Ohm's Law states that for devices obeying Ohm's Law, resistance is constant regardless of voltage or current.

• Typical conductors like metals obey Ohm's law, while devices like diodes and light bulbs may not.

• Resistor Construction: Resistance can be manipulated by combining resistors or altering the electric potential.

• Superconductors exhibit zero resistance, allowing current without energy loss.

• Protection Against Shock: Body resistance varies (high when dry, low when wet), affecting electric shock potential.

Diagramming Circuits

• Schematic Diagram: Uses symbols to represent circuit components.

• Ammeters measure current connected in series; voltmeters measure potential difference connected in parallel.

• Example Schematic Steps:

  1. Start with power source.

  2. Connect components sequentially, maintaining loops.

  3. Check accuracy of connections and circuit flow.

22.2 USING ELECTRICAL ENERGY

Energy Transfer in Electric Circuits

• Electrical energy is converted by various devices such as motors, lamps, and heaters into other useful forms of energy.

• Capacitors: Store electrical energy and release it when needed. Shown through charging and discharging behavior.

Thermal Energy Produced in Circuits

• Electrical energy transformed into thermal energy can be expressed as: $E = I^2Rt$ (energy = current² × resistance × time).

Example Problem: Thermal Energy

1. Heater Resistance: 10 $ ext{Ω}$, 120 V operating for 10 s.

   • Current through heater:

     • $I = rac{V}{R} = rac{120 ext{ V}}{10 ext{ Ω}} = 12.0 ext{ A}$

   • Thermal energy:

     • $E = I^2Rt = (12 ext{ A})^2(10 ext{Ω})(10 ext{ s}) = 14,400 ext{ J}$

Transmission of Electric Energy

• High-voltage transmission lines enable efficient energy transfer over long distances, minimizing Joule heating ($P = I^2R$).

• Increasing voltage decreases current across transmission lines, thus lowering I²R losses. Long-distance lines operate at higher voltages (over 500 kV).

• Example Impact: If a 41 A current passes through 1.4 Ω of wire resistance, $P = (41 ext{ A})^2 imes (1.4 ext{ Ω}) = 2400 ext{ W}$ wasted, illustrating improved efficiency through high voltage.

Kilowatt Hour

• Electric energy billing is in kilowatt-hours, where 1 kWh equals 3.6 × 10⁶ Joules. For a 1 kW device running for one hour, it consumes this amount of energy.

Example Problem: Operating Cost

1. Television Set: Operates at 2.0 A, 120 V, averages 7h/day for 30 days.

   • Power: $P = VI = (120)(2) = 240 ext{ W}$

   • Monthly energy consumption:

     • $E = P imes t = 240 ext{ W} imes (7 ext{ h/day} imes 30 ext{ days}) = 50400 ext{ Wh} = 50.4 ext{ kWh}$

   • Monthly cost:

     • 50.4 ext{ kWh} imes 0.11 ext{ $/kWh} = 5.544 ext{ $}

Summary of Key Concepts

• Battery, generator, and solar cells convert diverse energy forms to electrical energy.

• Current and resistance relationships are defined by Ohm's law, with significant implications for circuit design.

• Capacitors and energy conversion devices are key in utilizing electrical energy effectively.

• Efficient energy delivery mandates high-voltage systems limiting Joule losses, critical for modern electrical infrastructure.