/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 77 A galvanometer has a coil resist... [FREE SOLUTION] | 91影视

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Chapter 18: Problem 77

A galvanometer has a coil resistance of \(34.0 \Omega .\) It is to be made into a voltmeter with a full-scale deflection equal to \(100.0 \mathrm{V}\). If the galvanometer deflects full scale for a current of \(0.120 \mathrm{mA},\) what size resistor should be placed in series with the galvanometer?

Short Answer

Expert verified
Answer: The size of the resistor should be approximately 833299.33 惟.

Step by step solution

01

Determine the current needed for full-scale deflection

The current required to deflect the galvanometer full scale is given as \(0.120 \mathrm{mA}\). Let's convert it to Amperes to be consistent with the unit: \(0.120 \mathrm{mA} = 0.000120 \mathrm{A}\).
02

Calculate the total resistance of the voltmeter

Using Ohm's Law, we can calculate the total resistance needed for the voltmeter to have a full-scale deflection equal to \(100.0 \mathrm{V}\): \(V = IR\) \(R_{total} = \frac{V}{I}\) Plug in the values: \(R_{total} = \frac{100.0 \mathrm{V}}{0.000120 \mathrm{A}}\) \(R_{total} = 833333.33 \Omega\)
03

Calculate the size of the resistor to be placed in series with the galvanometer

Now, we have the total resistance needed, and we know the coil resistance of the galvanometer. The resistor required in series should bring the total resistance to the required value, so we just subtract the galvanometer's coil resistance from the total resistance: \(R_{resistor} = R_{total} - R_{coil}\) \(R_{resistor} = 833333.33 \Omega - 34.0 \Omega\) \(R_{resistor} = 833299.33 \Omega\) The size of the resistor to be placed in series with the galvanometer should be approximately \(833299.33 \Omega\).

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Most popular questions from this chapter

A source of emf \(\&\) has internal resistance \(r\), (a) What is the terminal voltage when the source supplies a current \(I ?\) (b) The net power supplied is the terminal voltage times the current. Starting with \(P=I \Delta V,\) derive Eq. \((18-22)\) for the net power supplied by the source. Interpret each of the two terms. (c) Suppose that a battery of emf 8 and internal resistance \(r\) is being recharged: another emf sends a current \(I\) through the battery in the reverse direction (from positive terminal to negative). At what rate is electric energy converted to chemical energy in the recharging battery? (d) What is the power supplied by the recharging circuit to the battery?
If a chandelier has a label stating \(120 \mathrm{V}, 5.0 \mathrm{A},\) can its power rating be determined? If so, what is it?
A \(500-\) W electric heater unit is designed to operate with an applied potential difference of \(120 \mathrm{V}\). (a) If the local power company imposes a voltage reduction to lighten its load, dropping the voltage to $110 \mathrm{V}$, by what percentage does the heat output of the heater drop? (Assume the resistance does not change.) (b) If you took the variation of resistance with temperature into account, would the actual drop in heat output be larger or smaller than calculated in part (a)?
A string of 25 decorative lights has bulbs rated at \(9.0 \mathrm{W}\) and the bulbs are connected in parallel. The string is connected to a \(120-\mathrm{V}\) power supply. (a) What is the resistance of each of these lights? (b) What is the current through each bulb? (c) What is the total current coming from the power supply? (d) The string of bulbs has a fuse that will blow if the current is greater than 2.0 A. How many of the bulbs can you replace with 10.4-W bulbs without blowing the fuse?
A Vespa scooter and a Toyota automobile might both use a \(12-\mathrm{V}\) battery, but the two batteries are of different sizes and can pump different amounts of charge. Suppose the scooter battery can pump 4.0 kC of charge and the automobile battery can pump \(30.0 \mathrm{kC}\) of charge. How much energy can each battery deliver, assuming the batteries are ideal?
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