Question

The reading of ammeter shown in figure is.... (A) \(2.18 \mathrm{~A}\) (B) \(3.28 \mathrm{~A}\) (C) \(6.56 \mathrm{~A}\) (D) \(1.09 \mathrm{~A}\)

Short answer

The ammeter reading cannot be accurately determined without further information on the circuit's specific configuration and values of components.

Step-by-step solution

Understand the problem

Read the problem carefully and gather the given information. In this exercise, we need to find the current flowing through an ammeter in a circuit with resistors. We will use the provided data and given circuit figure to analyze the problem.

Set up Ohm's law and Kirchhoff's laws

Write down Ohm's law and Kirchhoff's laws. Ohm's law states that the current (\(I\)) passing 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. Mathematically, it can be expressed as: \( V = I x R\) Kirchhoff's First Law (KCL), also known as the Current law, states that the total current entering a junction in an electric circuit is equal to the total current leaving the junction. Kirchhoff's Second Law (KVL), also known as the Voltage law, states that the algebraic sum of the potential differences (voltage) in any closed-loop or mesh in a network is equal to zero.

Apply Kirchhoff's laws to the circuit

Analyze the circuit and apply Kirchhoff's laws to create equations representing the behavior of the circuit. Since we're not given a specific circuit diagram, we'll need to make a few assumptions: 1. The circuit contains multiple resistors connected in series and parallel configurations. 2. The ammeter is connected in series with the entire circuit to measure the total current. 3. The total resistance in the circuit can be determined using the formulas for calculating equivalent resistance of resistors in series and parallel. With these assumptions, we can create the following equations: Using KCL: \(I_{total} = I_{1} + I_{2}\) Using KVL: \(V_{1} = I_{1} x R_{1}\) \( V_{2} = I_{2} x R_{2}\)

Solve for the ammeter reading

With the equations derived in Step 3, we can now solve for the unknown current, \(I_{total}\), which is the ammeter reading. Here, we assume values for our resistances and voltages based on the given options. Let's say: \(V_{1} = V_{2} = 10V\) \(R_{1} = 2Ω\) \(R_{2} = 4Ω\) Now we can solve for \(I_{1}\) and \(I_{2}\): \(I_{1} = V_{1} / R_{1} = 10V / 2Ω = 5A\) \(I_{2} = V_{2} / R_{2} = 10V / 4Ω = 2.5A\) Using KCL: \( I_{total} = I_{1} + I_{2} = 5A + 2.5A = 7.5A\) As we can see, our calculated value of 7.5A doesn't match any of the given options. This indicates that we need more information on the circuit's specific configuration and values of components to determine the correct ammeter reading.

Key concepts

Kirchhoff's laws

Kirchhoff's laws are fundamental principles used in circuit analysis. These rules help us understand how current and voltage behave in electric circuits. There are two main laws: Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL).

• **Kirchhoff's Current Law (KCL):** This law states that the total current flowing into a junction equals the total current flowing out. Think of it like traffic at an intersection; the number of cars going in must equal the number going out. This is crucial for managing how current separates or combines in complex circuits.
• **Kirchhoff's Voltage Law (KVL):** This law deals with voltage around a loop in a circuit. It says that the total sum of all voltage drops and rises around any closed loop must be zero. Imagine walking in a hilly area—you start and end at the same height after completing a circuit.

Understanding these laws helps you analyze how currents distribute and how voltages change around a circuit. They form the backbone of many electrical engineering tasks.

Ammeter reading

An ammeter is a device used to measure the current flowing through a circuit. Unlike other circuit components, an ammeter is always connected in series. This allows it to measure the total current flowing through a specific path or branch.

• **Importance of Ammeter in Circuit:** The primary role of an ammeter is to read the current in amperes. It's essential for diagnosing issues and ensuring circuits operate safely.
• **Reading Ammeter Values:** When taking ammeter readings, ensure it’s correctly placed in series with the load. This placement ensures the current flowing through it matches the circuit's load current.
• **Discrepancies in Readings:** If a measured value doesn’t align with expected results, re-check the connections and ensure all components' resistances and sources are known.

Accurate ammeter readings are vital for troubleshooting circuits and understanding how they'll behave under different conditions.

Series and parallel circuits

Identifying series and parallel circuits is essential for effective circuit analysis. Each type has unique properties concerning voltage and current distribution.

• **Series Circuits:** Components are arranged in a single path, so the same current flows through all. The total resistance is the sum of individual resistances. Voltage is divided among components. Think of water flowing through a single pipe.
• **Parallel Circuits:** Components are arranged so that the voltage across them is the same, but the current can vary. The reciprocal of the total resistance is the sum of reciprocals of individual resistances. Imagine multiple parallel lanes allowing traffic to flow at the same time.

Understanding these configurations helps determine the total resistance and predict how current and voltage behave in various circuits. They are foundational for designing and analyzing electrical systems.

Circuit analysis

Circuit analysis involves evaluating electrical circuits to understand current flow, voltage distribution, and power consumption. It combines mathematical methods with laws like Ohm's law and Kirchhoff's laws.

• **Ohm's Law:** This is crucial for circuit analysis as it defines the relationship between voltage, current, and resistance in a simple equation: \( V = IR \). It helps calculate any missing variable if two are known.
• **Role of Kirchhoff's Laws:** Together, KCL and KVL allow for setting up equations that aid in solving for unknown values in circuits, such as currents or voltages in complex networks.
• **Analyzing with Known Values:** When examining circuits, start by noting known variables. Use Ohm's law and Kirchhoff's laws to establish a system of equations that can be solved for unknowns.

A methodical approach to circuit analysis ensures all aspects of electrical operation are considered, leading to accurate predictions in real-world applications.