Physics Lecture Flashcards

Resistance

• Resistance is the property of a conductor that impedes the flow of electrons. Electrons bump into things which slows them down.
• Resistivity (\rho) is related to the density of these impediments.
• The resistance (R) of a conductor is determined by:
  • Resistivity (\rho)
  • Length (L)
  • Cross-sectional area (A)
• Formula: R = \rho \frac{L}{A}
• A wire can be both a conductor and a resistor.

Resistors

• Components in a circuit that provide specific resistance to current flow.

Series

• When two objects are connected end to end in a circuit, they are said to be in series.
• If resistors are in series:
  • The current is the same in each resistor (I1 = I2 = I_{eq}).
  • The voltage drop across each resistor adds up to the total voltage (V1 + V2 = V_{eq}).
  • Equivalent resistance is the sum of individual resistances: R{eq} = R1 + R_2
  • Adding Voltage: IR1 + IR2 = I(R1 + R2)
  • Adding Length: R{eq} = \rho(L1+L_2)/A

Parallel

• When two objects are in a circuit such that both ends of the object are connected, they are said to be in parallel.
• If resistors are in parallel:
  • The voltage drop across each resistor is the same and equal to the emf of the battery (V1 = V2 = V_{eq}).
  • The current splits and travels through each resistor separately (I1 + I2 = I_{eq})
  • The reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances: \frac{1}{R{eq}} = \frac{1}{R1} + \frac{1}{R_2}
  • Adding Current: V/R1 + V/R2 = V(1/R1 + 1/R2)

Ohm’s Law

• Relationship between voltage (V), current (I), and resistance (R) in a circuit.
• Formula: V = IR
• The more resistance, the less current can flow (higher resistance, lower current).
• I = \frac{V}{R}
• Units: Ohms (\Omega)

Electric Circuits

• A continuous conducting path through which charge can flow.
• Components include:
  • Electromotive force (emf) source (e.g., battery)
  • Resistors
  • Connecting wires

Current

• The net amount of charge flowing through a point in a circuit per unit time.
• Formula: I = \frac{\Delta q}{\Delta t}
• Units: Ampere (A) = Coulomb/second (C/s)
• Conventional current flows from the positive terminal to the negative terminal; electrons flow in the opposite direction.
• Current must be the same in all parts of a closed loop.
• If current is not the same, electrons will bunch up, resisting flow and naturally making the current constant.
• The system will naturally make the current constant, reaching a steady state.

Kirchhoff’s Laws

• Loop Law: The sum of the voltage drops around any closed loop in a circuit must equal zero.

Electromotive Force (emf)

• The maximum potential difference a battery or power source can provide.
• A car battery has an emf of 12 V.
• Symbol: Script E

Example Problem

• Calculate the current (I) in a simple circuit with an emf of 24 Volts and a resistance (R) of 8 \Omega
  • Using Ohm’s Law: V = IR
  • I = \frac{V}{R} = \frac{24}{8} = 3 Amps

Additional Concepts and Examples

• Electron Drift Speed: Although electrons move very slowly (fraction of a millimeter per second), a flashlight turns on instantly because electrons are already present in the wire.
• Light Bulb Example: The number of electrons entering a light bulb is equal to the number leaving. Light bulbs use the energy of electrons to emit light, not the electrons themselves. Charge is conserved.
• Plinko Analogy:
  • Disks represent electrons.
  • Bouncing through atoms represents resistance.
  • Angle of incline represents emf (potential difference).
• Wire Resistance: The connecting wires in a circuit generally have very small resistance, which can often be neglected.

Energy and Power

• The power dissipated by a resistor is: P = I^2R
• Or, in terms of the potential drop across the resistor: P = IV = \frac{V^2}{R}