Electrical Circuits: Ohm's Law and Resistance

Study Notes

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 (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

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 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

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 (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

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 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 (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)