Electricity and Circuits Notes

Fundamentals of Electricity

Electrical Quantities

• Electrical charge ($Q$) is a fundamental property of matter.

• Charge is measured in coulombs (C).

• When charges move or flow, it constitutes an electrical current ($I$), measured in amperes (A).

• Potential difference, also known as voltage ($V$), measures the energy provided to the charge and is measured in volts (V).

• The smallest quantity of charge is $1.6 × 10^{-19}$ C, which is the magnitude of the charge of an electron or proton.

• To increase power ($P$) delivered, one can either increase the energy ($E$) each particle carries or increase the number of particles arriving per second.

• Voltage ($V$) is the amount of energy per unit charge; 1 volt (V) equals 1 joule of energy per coulomb of charge.

• Current ($I$) is the rate of flow of charge; 1 ampere (A) is defined as 1 coulomb (C) of charge flowing per second.

Electric Circuits

• Electrical circuit analysis enables the calculation of physical quantities like charge ($Q$), current ($I$), voltage ($V$), energy ($E$), and power ($P$).

• Understanding what a volt and an ampere represent is crucial for performing this analysis.

Key Relationships (Formulas)

• Current: $I=\frac{Q}{T}$ (charge flow per unit time), where 1 ampere = 1 coulomb per second.

• Voltage: $V=\frac{e}{q}$ (energy per unit charge), where 1 volt = 1 joule per coulomb.

• Power: $P=\frac{e}{t}=VI$ (energy transferred per unit time), where 1 watt = 1 joule per second (or 1 ampere volt).

Worked Example

• A lamp in a circuit operates at 25 watts with a voltage of 5 volts across it and is turned on for 3 minutes (180 seconds).

  • To calculate the current flowing through the lamp: use $P = VI$, so $I=\frac{P}{V}=\frac{5}{25}{}=5A$ .

  • To calculate the amount of charge arriving at the lamp while it is on: use $I=\frac{Q}{T}$ , so $Q = It = 5 × 180 = 900 C$.

• Circuits facilitate the movement of electrical energy via the flow of charge.

  • Charge ($Q$): Measured in coulombs (C).

  • Current ($I$): $I = frac{Q}{t}$, 1 ampere = 1 coulomb per second.

  • Voltage ($V$): $V = frac{E}{Q}$, 1 volt = 1 joule per coulomb.

  • Power ($P$): $P = frac{E}{T} = VI$, 1 watt = 1 joule per second.

• Electrical circuit analysis allows the calculation of charge ($Q$), current ($I$), voltage ($V$), energy ($E$), and power ($P$).