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Ohm's Law is one of the fundamental principles used to calculate electrical quantities in electric circuits. Named after Georg Simon Ohm, this law establishes a direct relationship between voltage, current, and resistance in an electrical circuit. The formula is given by:\[ V = I \times R \]Where:

• \( V \) is the voltage across the circuit (in volts).
• \( I \) is the current flowing through the circuit (in amperes).
• \( R \) is the resistance in the circuit (in ohms).

In essence, Ohm's Law tells us that the amount of current passing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. This means that for a constant resistance, if the voltage increases, the current increases proportionally. Conversely, if the resistance increases, the current decreases, provided the voltage remains constant. Understanding Ohm's Law is crucial for analyzing any circuit and is especially useful when dealing with series and parallel resistor networks.

Power in electric circuits is the rate at which electrical energy is converted into another form, such as heat, light, or motion. The power consumed by a resistor in a circuit can be calculated using the formula:\[ P = I^2 \times R \]Alternatively, using Ohm's Law, we can express power in terms of voltage and current as:\[ P = V \times I \]Where:

• \( P \) is the power (in watts).
• \( I \) is the current through the resistor (in amperes).
• \( R \) is the resistance (in ohms).
• \( V \) is the voltage across the resistor (in volts).

The power calculation allows us to understand how much electrical energy is being used or dissipated by each resistor in the circuit. By computing power delivered to each resistor, as shown in the step-by-step solution, we can ensure that components in the circuit operate efficiently and safely, preventing overheating and potential damage.

Resistors in series are a common configuration in electric circuits, where the resistors are connected in a single path for the current to flow. In such setups, the same current flows through each resistor, but the voltage across each resistor may vary depending on its resistance.In a series circuit, the total resistance \( R_{\text{total}} \) is the sum of all individual resistances. Thus, for resistors \( R_1 \), \( R_2 \), and \( R_3 \) connected in series:\[ R_{\text{total}} = R_1 + R_2 + R_3 \]This series combination affects how the total current in the circuit is determined based on the total resistance. One key advantage of resistors in series is that it allows for easy division of voltage across each resistor, providing a simple way to distribute electrical energy.Understanding series circuits is essential as they are widely used in electronic devices and systems, where specific voltage levels are needed across different components for optimal operation.