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Chapter 19: Q28Q (page 796)

You are marooned on a desert island full of all kinds of standard electrical apparatus including a sensitive voltmeter, but you don’t have an ammeter. Explain how you could use the voltmeter to measure currents.

Short Answer

Expert verified

To convert a voltmeter to an ammeter, a small resistance is connected in parallel to it. The voltage reading of the voltmeter divided by the small resistance gives the current reading.

Step by step solution

01

Given data

A voltmeter is provided.

02

Parallel resistances

The equivalent resistance of multiple resistances connected in parallel is smaller than the smallest resistance connected.

03

Determination of the procedure to convert a voltmeter to an ammeter

A voltmeter has very high resistance and an ammeter has very low resistance. To negate the high resistance of the voltmeter, a small resistance is connected in parallel to it. The equivalent resistance is then very small. The voltage reading of the voltmeter divided by the small resistance connected in parallel gives the current reading because most of the current passes through the small resistance. Hence it can be used as an ammeter.

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Most popular questions from this chapter

For the circuit shown in figure 19.86, which consists of batteries with known emf and ohmic resistors with known resistance, write the correct number of energy-conservation and current node rule equations that would be adequate to solve for the unknown currents, but do not solve the equations. Label nodes and currents on the diagram, and identify each equation (energy or current, and for which loop or node).

Using thick connecting wires that are very good conductors, a Nichrome wire (“wire 1”) of length L₁ and cross-sectional area A₁ is connected in series with a battery and an ammeter (this is circuit 1). The reading on the ammeter is I₁. Now the Nichrome wire is removed and replaced with a different wire (“wire 2”), which is 2.5 times as long and has 5.5 times the cross-sectional area of the original wire (this is circuit 2). In the following question, a subscript 1 refers to circuit 1, and a subscript 2 refers to circuit 2. It will be helpful to write out your solutions to the following questions algebraically before doing numerical calculations. (Hint: Think about what is the same in these two circuits.)(a) What is the value of I₂/ I₁, the ratio of the conventional currents in the two circuits? (b) What is the value of R₂/ R₁, the ratio of the resistances of the wires? (c) What is the value of E₂/ E₁, the ratio of the electric fields inside the wires in the steady states?

The circuit shown in Figure 19.61 consists of two flashlight batteries, a large air-gap capacitor, and Nichrome wire. The circuit is allowed to run long enough that the capacitor is fully charged with $+ Q$ and $- Q$ on the plates.

Next you push the two plates closer together (but the plates don’t touch each other). Describe what happens, and explain why in terms of the fundamental concepts of charge and field. Include diagrams showing charge and field at several times.

A long Iron slab of width w and height h emerges from a furnace, as shown in Figure 19.79. Because the end of the slab near the furnace is hot and the other end Is cold, the electron mobility increases significantly with the distance x. The electron mobility is $u = u_{0} + k x$ where u₀is the mobility of the iron at the hot end of the slab. There are n iron atoms per cubic meter, and each atom contributes one electron to the sea of the mobile electron (we can neglect the small thermal expansion of the iron). A steady state conventional current runs through the slab from the hot end towards cold end, and an ammeter (not shown) measures the current to have a magnitude I in amperes. A voltmeter is connected to two locations a distance d apart, as shown. (a) Show the electric field inside the slab at two locations marked with $\times$ . Pay attention to the relative magnitudes of the two vectors that you draw. (b) Explain why the magnitude of the electric field is different at these two locations. (c) At a distance x from the left voltmeter connection, what is the magnitude of the electric field in terms x and the given quantities w, h, d, u₀, k, l, and n ( and fundamental constants)? (d) What is the sign of potential difference displayed on the voltmeter? Explain briefly. (e) In terms of the given quantitiesw, h, d, u₀, k, l, and n and ( and fundamental constants), what is the magnitude of the voltmeter reading? Check your work. (f) What is the resistance of this length of the iron slab?

A circuit consists of a battery, whose emf is K, and five Nichrome wires, three thick and two thin as shown in Figure 19.78. The thicknesses of the wires have been exaggerated in order to give you room to draw inside the wires. The internal resistance of the battery is negligible compared to the resistance of the wires. The voltmeter is not attached until part (e) of the problem. (a) Draw and label appropriately the electric field at the locations marked × inside the wires, paying attention to appropriate relative magnitudes of the vectors that you draw. (b) Show the approximate distribution of charges for this circuit. Make the important aspects of the charge distribution very clear in your drawing, supplementing your diagram if necessary with very brief written descriptions on the diagram. Make sure that parts (a) and (b) of this problem are consistent with each other. (c) Assume that you know the mobile-electron density n and the electron mobility u at room temperature for Nichrome. The lengths $(L_{1}, L_{2}, L_{3})$ and diameters $(d_{1}, d_{2})$ of the wires are given on the diagram. Calculate accurately the number of electrons that leave the negative end of the battery every second. Assume that no part of the circuit gets very hot. Express your result in terms of the given quantities $(K, L_{1}, L_{2}, L_{3}, d_{1}, d_{2}, n and u)$ . Explain your work and identify the principles you are using. (d) In the case that $d_{2} ≪ d_{1}$ , what is the approximate number of electrons that leave the negative end of every second? (e) A voltmeter is attached to the circuit with its + lead connected to location B (halfway along the leftmost thick wire) and its - lead connected to location C (halfway along the leftmost thin wire). In the case that $d_{2} ≪ d_{1}$ , what is the approximate voltage shown on the voltmeter, including sign? Express your result in terms of the given quantities $(K, L_{1}, L_{2}, L_{3}, d_{1}, d_{2}, n and u)$ .

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