Electrical Energy and Current Notes

Electrical Energy and Current

Section 1: Electric Force and Electric Potential

Coulomb's Law: Describes the force between two charged particles.
- The force is directly proportional to the magnitude of both charges.
- The force is inversely proportional to the square of the distance between the charges.
- Coulomb (C) is the SI unit of charge.
- $k_c = 8.99 \times 10^9 \text{ N} \cdot \text{m}^2/\text{C}^2$
Electrical Potential Energy:
- A uniform electric field exerts a force on a charged particle, moving it from point A to point B.
- A positively charged particle loses electric potential energy (PEelectric) as it moves in the direction of the electric force (similar to an object falling and losing gravitational potential energy PEg).
Potential Difference ( $\Delta V$ ):
- Defined as the change in electrical potential energy per coulomb of charge between two points.
- SI unit: joules/coulomb (J/C), also known as volts (V).
Batteries:
- Maintain a constant potential difference between their terminals (e.g., 1.5 V for AAA, AA, C, and D cells; 9.0 V; or 12 V for a car battery).
- In a 1.5 V battery, electrons gain 1.5 joules of energy per coulomb of charge as they move from the positive to the negative terminal, using chemical energy.
- When connected to a flashlight, electrons move through the bulb, losing 1.5 joules of energy per coulomb of charge.

Section 2: Capacitance

Capacitance:
- Measures the ability of a device (capacitor) to store electric charge.
- SI unit: coulombs/volt (C/V), also known as farads (F).

Section 3: Current and Resistance

Electric Current (I):
- Defined as the rate at which electric charges flow through an area.
- SI unit: coulombs/second (C/s), also known as amperes (A).
- $1 A = 6.25 \times 10^{18} \text{ electrons/second}$
Conventional Current:
- Defined as the flow of positive charge (even though in conducting wires, it's the negatively charged electrons that are moving).
- The flow of negative charge is equivalent to an equal amount of positive charge flowing in the opposite direction.
Resistance:
- Opposition to the flow of electric charge in a material.
- SI unit: volts/ampere (V/A), also known as ohms ( $\Omega$ ).
Ohm's Law:
- $\Delta V = IR$ (
- Relates potential difference ( $\Delta V$ ), current (I), and resistance (R).
- Valid only for certain materials where resistance remains constant over a wide range of potential differences.
Factors Affecting Resistance of a Wire:
- Length: Longer wire leads to greater resistance.
- Cross-sectional Area: Larger area (thicker wire) leads to less resistance.
- Material: Different materials (e.g., copper vs. iron) have different resistance.
- Temperature: Higher temperature generally leads to greater resistance.
Applications of Resistors:
- Resistors in circuits are used to control current.
- Variable resistors (potentiometers) are used in devices like dimmer switches and volume controls.
- Resistors on circuit boards regulate current to components.
Human Body Resistance:
- Ranges from approximately 500,000 $\Omega$ (dry) to 100 $\Omega$ (soaked with salt water).
- Currents under 0.01 A cause tingling.
- Currents greater than 0.15 A can disrupt the heart's electrical activity.

Section 4: Electric Power

Types of Current:
- Direct Current (DC):
  - Electrons flow in one direction only (e.g., from batteries).
- Alternating Current (AC):
  - Electrons vibrate back and forth (e.g., from generators).
  - Terminals switch signs (voltage alternates) at a specific frequency (e.g., 60 Hz in the US).
  - AC is better for transferring electrical energy over long distances.
Electric Power (P):
- Rate of energy consumption ( $\frac{\Delta PE}{\Delta t}$
- SI unit: joules/second (J/s), also known as watts (W).
- Formulas:
  - $P = I \Delta V$
  - Using Ohm's Law ( $\Delta V = IR$ ), we can derive:
    - $P = I^2R$
    - $P = \frac{{\Delta V}^2}{R}$
Household Energy Consumption:
- Power companies charge for energy consumed, typically measured in kilowatt-hours (kWh).
- 1 kWh is the energy consumed by a 1-kilowatt device operating for 1 hour.
- $1 \text{ kWh} = 3,600,000 \text{ J} = 3.6 \times 10^6 \text{ J}$
Electrical Energy Transfer:
- Energy is transferred from power plants to neighborhoods at high voltage and low current to minimize power loss in transmission lines.
- Power loss is given by $P = I^2R$ , so reducing current (I) significantly reduces power loss.
- Transformers are used to step up voltage and step down current for long-distance transmission, and then step down voltage and step up current for local distribution.
Electric Circuits:
- A circuit is a complete, closed-loop path that allows electrons to flow.
  - Closed circuit: A complete path, allowing current flow.
  - Open circuit: A broken path, preventing current flow.
Resistors in Series:
- Components are connected along a single path, so the same current flows through each resistor.
- Vbattery = V1 + V2 (Conservation of energy)
- Req = R1 + R2 (Equivalent resistance)
- Ibattery = I1 = I2 (Conservation of charge)
Resistors in Parallel:
- Components are connected across multiple paths, so the voltage drop across each resistor is the same.
- Ibattery = I1 + I2
- Vbattery = V1 = V2
Equivalent Resistance in Parallel:
- 1/Req = 1/R1 + 1/R2 + 1/R3 + ...
Wiring Lights (Series vs. Parallel):
- In a series circuit, if one bulb burns out, all bulbs go out because the circuit is broken.
- In a parallel circuit, if one bulb burns out, the other bulbs remain lit because they have their own independent paths.
- Parallel circuits maintain the brightness of each bulb as more bulbs are added, while series circuits become dimmer as more bulbs are added.
- Parallel circuits draw more current than series circuits (assuming identical bulbs).
Holiday Lighting Systems:
- Newer holiday lights use a bypass wire with higher resistance than filament. This ensures continuity and keeps other bulbs lit even if one filament fails. Under normal conditions, current flows through the filament due to its lower resistance.