Question

Three resistors, having values of 27.3 ohms \((\Omega), 4.0155 \Omega,\) and \(9.75 \Omega,\) are wired in series. What is the total resistance? (See Eq. 1062 which says that the total series resistance is the sum of the individual resistances.)

Short answer

Total resistance is 41.0655 \(\Omega\).

Step-by-step solution

Understand Series Resistance Concept

When resistors are wired in series, the total resistance is the sum of the individual resistances. This concept is given by the equation for total resistance in series (Eq. 1062).

Sum the Resistances

Add up the values of all resistors in series to get the total resistance. For the given resistors, calculate the sum: 27.3 \(\Omega\) + 4.0155 \(\Omega\) + 9.75 \(\Omega\).

Calculate Total Resistance

Combine the values obtained in step 2 to find the total resistance. Total Resistance, \(R_{total}\) = 27.3 \(\Omega\) + 4.0155 \(\Omega\) + 9.75 \(\Omega\) = 41.0655 \(\Omega\).

Key concepts

Understanding Electric Circuits

Electric circuits are the highways for electric current, allowing the flow of electricity through a complete path from the power source, through various electrical components, and back to its origin. It's essential to understand the role of different components in a circuit, as they influence the behavior of the electrical flow.

For example, in a simple series circuit where components are arranged end to end like beads on a string, the current is the same through all components, as it has just one path to follow. If the circuit is open or broken at any point, the flow of current is interrupted and the circuit ceases to function. Think of it like a water pipe system – if one pipe is blocked or cut, water cannot flow through the entire system.

It's beneficial for students to envision electricity in a physical manner, and metaphorical tools like the water pipe analogy can make a significant difference in understanding. Serialize your thoughts and start to picture how electric circuits are the foundational blueprints for electrical current flow.

Applying Ohm's Law to Circuit Problems

Ohm's Law, a fundamental principle in understanding electrical circuits, states that the current \(I\) flowing through a conductor between two points is directly proportional to the voltage \(V\) across the two points, and inversely proportional to the resistance \(R\) of the conductor. Formally, Ohm’s Law is expressed as \[ V = IR \].

When working with circuit problems, Ohm's Law can be a powerful tool to calculate unknown quantities when two are known. If resistance and voltage are known values in a circuit, you can calculate the current. Conversely, if current and resistance are known, you can determine the voltage required for the circuit. This calculation is often vital in both academic problems and real-world electrical engineering situations.

For a series circuit, in particular, knowing Ohm's Law is crucial, as the total voltage across the circuit is the sum of voltages across each component, and the current is constant throughout. Applying this law can provide clear insights into how different resistors in series will affect the overall behavior of the circuit.

The Role of a Resistor in Series Circuits

A resistor is a component of an electric circuit that opposes the flow of electrical current. It's a fundamental part for controlling the current flow, much like a valve controls the flow of water. In the context of series circuits, understanding the role of a resistor is crucial.

The total resistance of resistors in a series circuit is the sum of their individual resistances. This is because the current must pass through each resistor in turn, encountering the resistance of each. It's akin to running a marathon with multiple uphill segments; the total difficulty is the sum of each hill's challenge.

When calculating the total resistance in a series circuit, simply add up the resistance values of each resistor. Remember that the higher the resistance, the lower the current will be for a given voltage, according to Ohm's Law. Understanding the impact of resistors on an electric circuit's performance can significantly enhance your grasp of series resistance calculations and overall circuit analysis.