Electric Circuits

Electric Circuits Notes

20.1 Electromotive Force and Current

• Electrical Devices: Devices like radios, hair dryers, and computers rely on electric circuits for operation. Example: MP3 players powered by batteries.

• Electric Circuit: Energy source (battery) and energy-consuming device (like an MP3 player) are connected via conducting wires where electric charges move.

• Battery Functionality: Batteries create a chemical reaction that transfers electrons between terminals:

  • Positive Terminal: loses electrons, becomes positively charged.

  • Negative Terminal: gains electrons, becomes negatively charged.

• Electric Potential Difference: The difference in potential between the terminals of a battery, related to the electromotive force (emf). Typical values:

  • Car Battery: $8 - 12 V$

  • Flashlight Battery: $1.5 V$

• Current Definition: The flow of charge through a surface per unit time, defined as $I = rac{ ext{Charge}}{ ext{Time}}$.

  • Unit of Current: $1 ext{ Ampere (A)} = 1 ext{ Coulomb/second (C/s)}$.

• Types of Current:

  • Direct Current (dc): Current flows in one direction (e.g., batteries).

  • Alternating Current (ac): Current changes direction periodically (e.g., power from generators).

• Example Calculation: Current of a calculator with $3.0 V$ and $0.17 mA$:

  • Charge in 1 hour: $Q = 0.17 imes 10^{-3} ext{ A} imes 3600 ext{ s} = 0.61 ext{ C}$.

  • Energy delivered: $Energy = Charge imes Voltage = (0.61 C)(3 J/C) = 1.83 J$.

20.2 Resistance and Resistivity

• Resistor Definition: A component that limits the flow of electric current in a circuit.

  • Resistivity ($ ho$): Material-specific property impacting resistance, defined as:
    $R = <br>ho rac{L}{A}$ where $R$ = resistance, $L$ = length, $A$ = cross-sectional area.

• Materials:

  • Conductors (e.g., copper) have low resistivity.

  • Insulators (e.g., rubber) have high resistivity.

  • Semiconductors have intermediate values.

• Example Application: A flashlight with a filament connected to a $3.0 V$ battery delivering $0.40 A$ results in:
  $R = rac{V}{I} = rac{3.0 V}{0.40 A} = 7.5 \Omega$.

20.3 Conventional Current vs. Electron Flow

• Customarily, current is treated as flowing from positive to negative (conventional current), even though electrons flow negatively in a circuit.

• Ohm’s Law: Defines the relationship between voltage, current, and resistance:
  $V = IR$ where $V$ = voltage, $I$ = current, $R$ = resistance.

20.4 Electric Power

• Power in Circuits: The rate at which electrical energy is transferred by an electric circuit, calculated as:
  $P = IV$, where $P$ = power (in watts), $I$ = current (A), $V$ = voltage (V).

• Power in resistors can also be computed using:
  $P = I^2R$ or $P = rac{V^2}{R}$.

20.5 AC vs DC Circuits

• AC circuits involve current that periodically reverses direction, unlike DC where current flows in one direction.

• Average Power in AC Circuits: Given as:
  $\bar{P} = rac{1}{2} P_{peak}$ resulting from fluctuating current and voltage.

20.6 Series and Parallel Circuits

• Series Circuit: Current remains the same across all devices. Total resistance is the sum of resistances:
  $R<em>s = R</em>1 + R_2 + …$.

  • Example Calculation: An $R<em>1 = 47 \Omega$, $R</em>2 = 86 \Omega$, $V = 24 ext{ V}$ gives:

  • $I = rac{V}{R_s}$

• Parallel Circuit: Voltage across each device is the same. Total resistance is calculated using:
  $rac{1}{R<em>p} = rac{1}{R</em>1} + rac{1}{R_2} + …$.

20.7 Internal Resistance

• Internal Resistance in Batteries: Batteries also provide resistance. The voltage across terminals differs when current is drawn, leading to a terminal voltage less than the nominal emf due to internal resistance.

• Example Problems relate to calculating equivalent resistances, total current, and power in mixed circuit configurations.