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1. Intro to Physics Units1h 29m
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5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
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10. Conservation of Energy2h 54m
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21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
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24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
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32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

27. Resistors & DC Circuits

Solving Resistor Circuits

Physics

27. Resistors & DC Circuits

Solving Resistor Circuits

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6:10 minutes

Problem 60

Textbook Question

A milliammeter reads 25 mA full scale. It consists of a 0.20-Ω resistor in parallel with a 33-Ω galvanometer. How can you change this ammeter to a voltmeter giving a full scale reading of 25 V without taking the ammeter apart? What will be the sensitivity (Ω/V) of your voltmeter?

Verified step by step guidance

Understand the problem: We are tasked with converting an ammeter into a voltmeter. The ammeter has a full-scale current of 25 mA and consists of a 0.20-Ω resistor in parallel with a 33-Ω galvanometer. To convert it into a voltmeter, we need to add a series resistor such that the voltmeter gives a full-scale reading of 25 V when the current through the ammeter is 25 mA.

Step 1: Calculate the total resistance of the ammeter. Since the 0.20-Ω resistor is in parallel with the 33-Ω galvanometer, the equivalent resistance $ R_{eq} $ can be calculated using the formula: $ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} $, where $ R_1 = 0.20 \ \Omega $ and $ R_2 = 33 \ \Omega $.

Step 2: Determine the series resistor $ R_s $ needed to convert the ammeter into a voltmeter. The total resistance of the voltmeter $ R_{total} $ must satisfy Ohm's Law: $ V = I \cdot R_{total} $, where $ V = 25 \ \text{V} $ and $ I = 25 \ \text{mA} $. Since $ R_{total} = R_{eq} + R_s $, solve for $ R_s $ using $ R_s = \frac{V}{I} - R_{eq} $.

Step 3: Calculate the sensitivity of the voltmeter. Sensitivity is defined as the resistance per volt ($ \Omega/V $) of the voltmeter. It can be calculated as $ \text{Sensitivity} = \frac{R_{total}}{V} $, where $ R_{total} = R_{eq} + R_s $.

Step 4: Summarize the results. The series resistor $ R_s $ is the key component to convert the ammeter into a voltmeter, and the sensitivity provides a measure of how the voltmeter responds to voltage changes. Ensure all calculations are consistent with the given values and units.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ammeter and Voltmeter Functionality

An ammeter measures current in a circuit, while a voltmeter measures voltage across two points. To convert an ammeter into a voltmeter, one must understand the relationship between current, voltage, and resistance, as well as how to configure the circuit components to achieve the desired measurement range.

Ohm's Law

Ohm's Law states that the current (I) 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. This relationship is expressed as V = IR, which is fundamental in calculating the necessary resistance to convert an ammeter into a voltmeter.

Sensitivity of a Voltmeter

The sensitivity of a voltmeter, expressed in ohms per volt (Ω/V), indicates how much resistance the voltmeter presents per volt of measurement. A higher sensitivity means the voltmeter has a higher internal resistance, which minimizes its impact on the circuit being measured, thus ensuring accurate voltage readings.

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