Electrical Circuits: Ohm's Law and Resistance

Ohm's Law

• Relates voltage, current, and resistance in a conductor: V = I × R
• States that the current flowing through a conductor is directly proportional to the voltage applied across it, provided the resistance remains constant
• Mathematically represented as: I = V/R or R = V/I

Resistance and Resistivity

• Resistance (R): opposition to the flow of electric current, measured in ohms (Ω)
• Resistivity (ρ): inherent property of a material, independent of its shape and size, measured in ohm-meters (Ωm)
• Resistivity depends on the material, temperature, and other factors
• Formula: R = ρ × L / A, where L is the length and A is the cross-sectional area of the conductor

Electric Circuits

• A path through which electric current flows
• Consists of various components, such as resistors, capacitors, and sources of electromotive force (emf)
• Can be classified into:
  • Series circuits: components connected one after the other, current flows through each component
  • Parallel circuits: components connected between the same two points, voltage across each component is the same

Series and Parallel Connections

• Series Connection:
  • Total resistance: Rtotal = R1 + R2 + ... + Rn
  • Total voltage: Vtotal = V1 + V2 + ... + Vn
  • Current: I is the same throughout the circuit
• Parallel Connection:
  • Total resistance: 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn
  • Total voltage: Vtotal = V is the same across each component
  • Current: I = I1 + I2 + ... + In

Electric Power and Energy

• Electric Power (P): rate of energy transfer, measured in watts (W)
• Electric Energy (E): total energy transferred, measured in joules (J)
• Formula: P = VI, where V is the voltage and I is the current
• Energy consumption: E = Pt, where t is the time
• Units of power: kW (kilowatt), MW (megawatt), GW (gigawatt)
• Units of energy: Wh (watt-hour), kWh (kilowatt-hour), MWh (megawatt-hour)

Ohm's Law

• Relates voltage, current, and resistance in a conductor using the formula: V = I × R
• Describes the direct proportionality between voltage and current, with resistance as the constant of proportionality

Resistance and Resistivity

• Resistance (R): measured in ohms (Ω), opposes the flow of electric current
• Resistivity (ρ): inherent property of a material, measured in ohm-meters (Ωm), dependent on material, temperature, and other factors
• Formula: R = ρ × L / A, where L is the length and A is the cross-sectional area of the conductor

Electric Circuits

• A path through which electric current flows, composed of various components
• Classified into:
  • Series circuits: components connected one after the other, with current flowing through each component
  • Parallel circuits: components connected between the same two points, with voltage across each component being the same

Series and Parallel Connections

• Series Connection:
  • Total resistance is the sum of individual resistances: Rtotal = R1 + R2 +...+ Rn
  • Total voltage is the sum of individual voltages: Vtotal = V1 + V2 +...+ Vn
  • Current is the same throughout the circuit: I
• Parallel Connection:
  • Total resistance is the reciprocal of the sum of individual reciprocals: 1/Rtotal = 1/R1 + 1/R2 +...+ 1/Rn
  • Total voltage is the same across each component: Vtotal = V
  • Current is the sum of individual currents: I = I1 + I2 +...+ In

Electric Power and Energy

• Electric Power (P): rate of energy transfer, measured in watts (W), calculated using the formula: P = VI
• Electric Energy (E): total energy transferred, measured in joules (J), calculated using the formula: E = Pt
• Units of power: kW (kilowatt), MW (megawatt), GW (gigawatt)
• Units of energy: Wh (watt-hour), kWh (kilowatt-hour), MWh (megawatt-hour)