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Chapter 12: Problem 1737

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

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

Step by step solution

01

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.
02

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.
03

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: \(V_{1} = I_{1} x R_{1}\) \( V_{2} = I_{2} x R_{2}\)
04

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.

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