Key Concepts in Electrical Circuits and Laws

Fundamentals of Electric Current and Circuits

Electric Current

Electric current involves the movement of electric charges through a material or gas. An electric circuit is the path through which electric current flows. A complete circuit must contain:

• Generators
• Receivers (Loads)
• Interconnects (Conductors)

Potential Difference (Voltage)

Potential difference (Voltage) is the energy necessary to move a unit positive charge from one point to another. It is measured in volts (V).

Voltmeter

A voltmeter is an apparatus used to measure the potential difference between two points in a circuit.

Current Intensity

Electric current intensity is the amount of charge passing through a section of a conductor per unit of time. The unit is the ampere (A).

Ammeter

An ammeter is used to measure the current intensity passing through a point in a circuit.

Ohm's Law

The electric intensity flowing through a conductor is directly proportional to the voltage applied across its ends (Ohm's Law).

Electrical Resistance

Electrical resistance is the difficulty encountered by electrons in their motion through a conductor.

Conservation Principle of Energy

The energy supplied by the generator is equal to the total energy transformed in each receiver plus the energy dissipated as heat.

Joule's Law

The electrical energy dissipated as heat is directly proportional to:

• The value of the resistance (R)
• The square of the intensity (I²)
• The time (t) the current flows

Electrical Power and Energy

Electrical power is the energy transformed per unit of time. Common units for electrical energy include the kilowatt-hour (kWh).

Calculations and Examples

Potential Difference Calculation

Calculate the potential difference between two points when a load of 2 Coulombs (C) moves, requiring 40 Joules (J) of energy:

$$V = E/Q = 40 \text{ J} / 2 \text{ C} = 20 \text{ Volts}$$

Energy Calculation

Calculate the energy needed to move a charge of 0.3 C with a potential difference of 50 V:

$$V = E/Q \implies E = V \times Q = 50 \text{ V} \times 0.3 \text{ C} = 15 \text{ Joules}$$

Charge Calculation from Current

Calculate the charge passing through a filament bulb in one hour if the current is 300 mA (0.3 A):

$$I = Q/t \implies Q = I \times t$$

Time in seconds: $1 \text{ hour} = 3600 \text{ seconds}$.

$$Q = 0.3 \text{ A} \times 3600 \text{ s} = 1080 \text{ Coulombs}$$

Number of Electrons Calculation

How many electrons cross a point every minute if the current is 2 $\mu$A ($2 \times 10^{-6}$ A)?

Time in seconds: $1 \text{ minute} = 60 \text{ seconds}$.

1. Calculate total charge (Q):

$$Q = I \times t = (2 \times 10^{-6} \text{ A}) \times 60 \text{ s} = 1.2 \times 10^{-4} \text{ C}$$

2. Calculate the number of electrons ($N_e$): (Using $1 \text{ electron charge} \approx 1.602 \times 10^{-19} \text{ C}$, or $Q = N_e \times e$)

$$N_e = Q / e = (1.2 \times 10^{-4} \text{ C}) / (1.602 \times 10^{-19} \text{ C/electron}) \approx 7.49 \times 10^{14} \text{ electrons}$$

Resistance Calculation (Ohm's Law)

Calculate the resistance of a circuit with a current of 2.5 A and a voltage of 125 V:

$$R = V / I = 125 \text{ V} / 2.5 \text{ A} = 50 \text{ Ohms}$$

Current Intensity Calculation

Calculate the current intensity through a conductor with a resistance of 20 $\Omega$ and a potential difference of 9 V:

$$I = V / R = 9 \text{ V} / 20 \Omega = 0.45 \text{ A}$$

Resistance Calculation (Resistivity Formula)

Calculate the resistance of a wire given resistivity ($\rho$), length (L), and cross-sectional area (S):

Given: $\rho = 1.05 \times 10^{-6} \ \Omega\cdot\text{m}$, $L = 120 \text{ m}$, $S = 2.5 \times 10^{-6} \text{ m}^2$.

$$R = \rho L / S = (1.05 \times 10^{-6} \times 120) / (2.5 \times 10^{-6}) = 50.4 \text{ Ohms}$$

Current Calculation using Power

Calculate the current (I) in a circuit connected to a 220 V source, assuming the resistance is $50.4 \Omega$:

$$V = I \times R \implies I = V / R = 220 \text{ V} / 50.4 \Omega \approx 4.36 \text{ Amps}$$

Resistance Calculation from Power Data

Calculate the resistance of a bulb connected to a 220 V network drawing a current of 270 mA (0.27 A):

$$R = V / I = 220 \text{ V} / 0.27 \text{ A} \approx 814.8 \text{ Ohms}$$

Current Calculation from Resistance and Voltage

Calculate the current (I) if the resistance is estimated at 100 $\Omega$ and the potential difference is 6 V:

$$R = V/I \implies I = V/R = 6 \text{ V} / 100 \Omega = 0.06 \text{ A}$$

Calculate the charge (Q) passing in 60 seconds:

$$I = Q/t \implies Q = I \times t = 0.06 \text{ A} \times 60 \text{ s} = 3.6 \text{ C}$$

Electrical Energy Calculation (Joule Effect)

Calculate the electrical energy dissipated as heat (Joule effect) over 200 $\Omega$ with a current of 30 mA (0.03 A) for 1 hour (3600 s):

$$E = I^2 R t = (0.03 \text{ A})^2 \times 200 \Omega \times 3600 \text{ s} = 648 \text{ Joules}$$

Appliance Power and Energy

For a washer operating at 220 V with a power consumption of 2100 W:

a) Calculate the current (I):

$$P = V \times I \implies I = P / V = 2100 \text{ W} / 220 \text{ V} \approx 9.55 \text{ A}$$

b) Calculate the energy (E) consumed in one hour (3600 s):

$$P = E/t \implies E = P \times t = 2100 \text{ W} \times 3600 \text{ s} = 7,560,000 \text{ Joules}$$