91Ó°ÊÓ

In the realm of electrical circuits, the concept of electrical power is fundamental. Electrical power is the rate at which electrical energy is transferred by an electric circuit. It is measured in watts (W). Power in a circuit is often described by the formula:\[ P = V \times I \]where:

• \( P \) stands for power in watts
• \( V \) represents voltage in volts
• \( I \) is current in amperes

This means that power can be calculated by multiplying the voltage and current in the circuit. In our exercise, the 60 W lamp converts electrical energy into light and heat. By knowing the power and voltage of the lamp, we can determine the current flowing through it, which is a critical step in solving the overall exercise problem.

A series circuit is an electrical circuit in which components are connected along a single path. This means the same current flows through each component in the circuit. In our exercise, the lamp and the resistor are connected in series. This configuration affects how you calculate different parameters such as voltage, current, and resistance. In a series circuit:

• The total voltage across the circuit is the sum of the voltages across each component.
• The current remains the same through each component.
• The total resistance is the sum of individual resistances.

Understanding the setup of a series circuit is essential when solving for the unknown resistance in this exercise, especially when you need to allocate the total voltage supply to each component.

Voltage drop refers to the reduction in voltage across a component in a circuit. For components in series, the voltage supplied is divided among them, based on their resistance. In our exercise, we see a total voltage of 120 V from the source that drops as it is divided between a lamp and a resistor in series.The formula for calculating voltage drop across a component is the same as Ohm’s Law:\[ V = I \times R \]where:

• \( V \) is the voltage across the component
• \( I \) is the current flowing through the circuit
• \( R \) is the resistance of the component

In this exercise, once we calculate the voltage across the lamp (25 V), we subtract this from the total voltage (120 V) to find the voltage drop across the resistor.

Resistance is a measure of how much a component resists the flow of current in a circuit. It is measured in ohms (Ω). When we calculate resistance, we refer to Ohm's Law, which relates voltage (\( V \)), current (\( I \)), and resistance (\( R \)) as:\[ V = I \times R \]To find the resistance of a component, rearrange the formula:\[ R = \frac{V}{I} \]For our exercise, after determining that the voltage across the resistor is 95 V and the current through the circuit is 2.4 A, we can plug these values into the formula:\[ R = \frac{95.0}{2.4} \approx 39.58 \, \Omega \]Thus, the resistance of the resistor is approximately 39.58 Ω. This calculation is the final step in fully understanding the behavior and constraints of the series circuit in the exercise.