In this explainer, we will learn how to describe the construction of ammeters using the thermal expansion of conducting wires to measure alternating currents.
Ammeters are circuit components used to measure current.
Ammeters used in direct current (dc) circuits are often constructed using a galvanometer. This device uses a needle deflected by magnetic torque to indicate current magnitude and direction.
In alternating current (ac) circuits, the galvanometer is ill-suited to respond to repeated, rapid changes in current direction. A different ammeter design is called for.
Hot-wire ammeters are devices that measure current based on the thermal expansion of a wire. The direction of current in the wire is unimportant, making hot-wire ammeters well-suited for ac circuits.
Consider an ac circuit with a hot-wire ammeter in series, as shown in the following figure.
The ammeter is constructed so that it splits current across two parallel branches. One branch consists of a resistor known as a shunt resistor. The other branch includes the wire that is heated, as follows.
Individual charges entering the ammeter will flow through either the shunt resistor or the hot wire.
When a charge flows through the wire, the temperature of the wire increases and the wire expands.
The red line in the diagram represents a nonconducting string tied to the hot wire. The string is under tension due to the spring. When the temperature of the wire increases, the wire lengthens and the string is pulled to the right.
The moving string rotates a pulley, pulling a needle across a calibrated measurement scale. The position of the needle on the scale indicates the ammeter’s current reading.
Example 1: Explaining How Alternating Current Can Lead to a Constant Current Reading in a Hot-Wire Ammeter
The platinum–iridium alloy wire in a hot-wire ammeter expands when its temperature increases and contracts when its temperature decreases. The temperature of the wire is dependent on the current in the wire. A hot-wire ammeter using such a wire will give a constant reading for an alternating current that has a particular peak value. Which of the following most correctly explains how an alternating current with a frequency of 50 Hz in the wire can produce a constant hot-wire ammeter reading?
- The frequency at which the wire can undergo a cycle of expansion and contraction is much smaller than the frequency of the alternating current, so the expansion of the wire corresponds to the effective value of the current.
- The wire expands when its temperature increases much faster than it contracts when its temperature decreases, so the wire never reduces in temperature for a sufficient time to contract noticeably.
- The wire heats a hot-wire ammeter’s other mechanical components. The expansion and contraction of these components are out of phase with each other, so the reading on the ammeter remains constant.
The expansion of the platinum–iridium wire depends on the amount of charge flowing through it. The stronger the current is, the more the temperature of the wire is increased by resistance to the flowing charge and the more the wire expands.
Even though dissipated electrical energy continually tends to increase the wire’s temperature, the wire does not lengthen without limit.
The more the temperature of the wire exceeds the temperature of its surroundings, the greater the rate at which the wire radiatively heats its surroundings is.
At a certain temperature, the tendency of the wire temperature to increase due to dissipation of electrical energy and its tendency to decrease due to the wire heating its surroundings are equal.
At this temperature, the rates of energy transfer to and from the wire are equal. The wire therefore maintains this temperature, at which point the wire is in thermal equilibrium.
A wire at a constant temperature maintains a constant length. This allows a stable reading of current to occur.
In this example, we are told that the temperature of the wire depends on the current in it.
The current alternates at a rate of 50 Hz, or 50 cycles every second. One such cycle is depicted below.
Regardless of current being positive or negative, at all points where current is nonzero, dissipated energy tends to increase the temperature of the wire, increasing its length.
Note that the length of the wire will never decrease. Rather, it will increase until it reaches the length it would have if it was carrying a direct current with the same magnitude as the effective value of the alternating current. When this occurs, the rates of energy transfer to and from the wire are equal.
Option B makes the claim that, in addition to expanding due to an increase in temperature, the wire also contracts if its temperature decreases. However, we have established that the wire temperature does not ever decrease, so option B cannot be correct.
Option C describes heating of the other mechanical components in the ammeter, such as the string, spring, and pulley.
Specifically, it is claimed that these components expand and contract in such a coordinated way that the system overall reaches an equilibrium state.
Alternating current ammeters are not designed with this property in mind, however. Intuitively, it is more to be expected that heating or cooling the ammeter’s mechanical parts will make them expand or contract in unison, preventing a constant reading.
The most correct explanation of the ammeter’s ability to deliver a constant reading for a current alternating at 50 Hz is option A.
Example 2: Identifying a Nonconducting Component of a Hot-Wire Ammeter
The diagram shows a hot-wire ammeter. Which of the components shown is attached to electrically conductive components but is not itself electrically conductive?
Component II in the diagram is the platinum–iridium wire that heats and expands as charge flows through it. It is a conductor but is attached to a nonconducting string represented in the diagram by the red line.
The string puts tension on the wire without affecting the flow of charge through it. This nonconductive component is labeled component III.
Example 3: Identifying the Condition of a Hot-Wire Ammeter to Read a Constant Current
Which of the following conditions must apply for a hot-wire ammeter to give a constant reading for an alternating current?
- The wire must heat its surroundings with the same power that it is heated with by its surroundings.
- The electrical power dissipated by the wire must equal the power with which the wire heats its surroundings.
- The electrical power dissipated in the wire must be greater than the power with which the wire heats its surroundings.
- The electrical power dissipated in the wire must be zero.
When a hot-wire ammeter gives a constant reading, we know the needle indicating that reading is stationary.
This means that the string wrapped over the pulley that determines how the needle points is also not moving.
The string’s stillness tells us that the wire to which it is tied is neither expanding nor contracting. Therefore, its temperature is constant—the wire is in thermal equilibrium.
Assuming the ammeter is measuring a nonzero current, the wire’s thermal equilibrium is due to a balance between the tendency for the temperature to increase and the tendency for it to decrease.
The temperature of the wire tends to increase as it dissipates electrical power in the circuit. When the wire transfers energy to its surroundings at the same rate at which energy is transferred to it by dissipation, thermal equilibrium is achieved and the ammeter reads a constant current.
This description aligns with option B.
Note that choice A describes the wire heating its surroundings and the surroundings heating the wire at equal rates. In reality, these rates are not the same; the net transfer of dissipated energy is from the wire to its surroundings.
Option C claims that a constant ammeter reading reflects more power being dissipated in the wire than transferred to its surroundings. However, this condition would cause the wire temperature to increase, increasing its length and leading to a reading that increases over time.
If the electrical power dissipated by the wire is zero, as described in option D, no charge flows through it. Zero current would be indicated by a constant current reading of amperes.
However, this is not a necessary condition for a constant reading; the ammeter is capable of reading a constant current even if power is dissipated in the wire, as described in choice B. That option is our final answer to this question.
We have seen that the energy dissipated in a hot-wire-ammeter depends on the current in the wire. Specifically, if is the energy dissipated by the wire and is the current,
The deflection of the ammeter arm, while directly proportional to the energy dissipated, , is not directly proportional to the current .
Increasing the current in the wire from amperes to one ampere will deflect the ammeter needle through an angle we will call . Changing the current from one ampere to amperes will deflect the needle through a different angle we will call , where is greater than .
For successive equal increments of the current, the associated ammeter needle deflection angle will be greater than that for the preceding increment.
Example 4: Choosing Correct Scale Divisions of a Hot-Wire Ammeter
Which of the following diagrams most correctly shows the divisions of the scale of a hot-wire ammeter corresponding to equal changes in current?
In a hot-wire ammeter, the energy dissipated by the wire is proportional to the square of the current.
Therefore, if current is incremented, each additional increment will dissipate more energy than the previous increment. The scale markings for current readings reflect this.
For example, markings between one ampere and amperes are separated by a greater distance than those between amperes and one ampere. The distance between the markings indicating two and amperes is greater still, and so on.
Therefore, a scale for equal increments of current will display markings separated by increasing distance for increasing current. The diagram that shows this most correctly is diagram C.
Diagram A, displaying equal spacings between equal changes in current, would be correct if the energy dissipated by the hot wire was proportional simply to current, rather than current squared.
Choice B suggests an inverse relationship between dissipation and current, leading to markings separated by smaller distances as current increases.
Because energy dissipated by the hot wire is proportional to current squared, we choose diagram C as the best indicator of the scale divisions on a hot-wire ammeter.
- A hot-wire ammeter is designed to measure alternating currents.
- The ammeter works by correlating the thermal expansion of a wire with current in the wire.
- When the wire is in thermal equilibrium, the ammeter reads a constant current.
- The scale of a hot-wire ammeter is nonlinear because incremental increases in current lead to progressively larger deflections of the needle indicating current.