Current Electricity: Ohm's Law, Series and Parallel Circuits, Resistance, Power, Energy, and Kirchhoff's Laws

Current Electricity: Series and Parallel Circuits, Resistance, Power, and Energy

Ohm's Law

Ohm's Law is a fundamental law in electronics that relates voltage, current, and resistance in a circuit. It is given by the formula $$I = V / R$$, where:

• $$I$$ is the current in amperes
• $$V$$ is the voltage in volts
• $$R$$ is the resistance in ohms

This law allows us to calculate the current when we know the voltage and resistance in a circuit.

Series and Parallel Circuits

In a series circuit, the same amount of current flows through each component in the circuit. All quantities (voltage, current, resistance, and power) must relate to each other in terms of the same two points in a circuit. In a parallel circuit, all components share the same electrical nodes, and the voltage is the same across all parallel components. The total current in a parallel circuit is the sum of all the individual branch currents.

Series Circuit Example

Consider a series circuit with a 6.349 mA current, a 2.984 V voltage, and a 470 Ω resistance. Using Ohm's Law, we can calculate the total resistance of the series circuit: $$R_{total} = \frac{V_{total}}{I_{total}} = \frac{2.984 \text{ V}}{6.349 \text{ mA}} = 470 \Omega$$.

Parallel Circuit Example

In a parallel circuit, the total current in the circuit is the sum of the individual branch currents. For example, if we have a parallel circuit with three resistors (15 Ω, 220 Ω, and 470 Ω), we can use the formula $$I_{total} = \frac{I_1 I_2 I_3}{R_1 + R_2 + R_3}$$ to find the total current when a 9 V voltage is applied across the circuit.

Electrical Resistance

Resistance is a measure of the opposition a material offers to the flow of electric current. It is usually denoted by the letter "R" and is measured in ohms (Ω). The total resistance of a series circuit is equal to the sum of the individual resistances, while the equivalent resistance of a parallel circuit is given by the formula $$R_{equiv} = \frac{1}{1 + R_1 + R_2 + \cdots}$$, where $$R_1$$, $$R_2$$, etc., are the individual resistances.

Electric Power and Energy

Electric power is the product of voltage and current in a circuit. It is calculated using the formula $$P = V \times I$$, where:

• $$P$$ is the power in watts (W)
• $$V$$ is the voltage in volts (V)
• $$I$$ is the current in amperes (A)

Electric energy is the product of power and time. It is calculated using the formula $$E = P \times t$$, where:

• $$E$$ is the energy in joules (J)
• $$P$$ is the power in watts (W)
• $$t$$ is the time in seconds (s)

Kirchhoff's Laws

Kirchhoff's Laws are a set of rules that help analyze electrical circuits. They are:

1. Kirchhoff's Current Law (KCL): The sum of all currents going into a junction is equal to the sum of currents going out of the junction.
2. Kirchhoff's Voltage Law (KVL): The sum of all voltage drops in a closed loop is equal to the sum of voltage sources in the loop.

These laws, along with Ohm's Law, provide a solid foundation for analyzing and understanding electrical circuits, including series and parallel circuits, resistance, power, and energy.