What is a 1/2 digit on a DMM?

Partial extended accuracy on lower part of the range.

For more information, please see Electronics Notes for the article on What is a DMM, Digital Multimeter?

Also, please see Fluke site for the article on What is a digital multimeter? How to use a multimeter

YouTube Video: View Science Buddies channel for the video on How to Use a Multimeter

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A 50 microampere meter movement has an internal resistance of 2,000 ohms. What applied voltage is required to indicate half-scale deflection?

0.05 volts.

From wp2ahg:

50 microamps is full scale. Half scale would be 25 microamps.

Use Ohm's Law to calculate voltage:

  \[\text{Volts} = \frac{25\text{ micro amperes}}{1,000,000\text{ amperes}}\times{2,000 \text{ ohms}}\]

\[\text{Volts} = 0.05\text{ volts}\]

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What is the purpose of a series multiplier resistor used with a voltmeter?

It is used to increase the voltage-indicating range of the voltmeter.

The current in the series of multiplier resistor circuits divides itself, based on resistor rating. The division of the current increases (multiplies) the range of the voltmeter.

For well-illustrated explanation, please see All About Circuits site Voltmeter Design

Also, Tutorials Point article DC Voltmeters, paragraph Multi Range DC Voltmeter

And, Electronics Tutorials site for the article Voltmeter

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What is the purpose of a shunt resistor used with an ammeter?

It is used to increase the ampere indicating range of the ammeter.

From EE Power site for the article on Definition Shunt Resistor

"A shunt resistor is used to measure electric current, alternating or direct. This is done by measuring the voltage drop across the resistor."

The Ohm's law is used in shunt resistor to determine the current level. It creates low resistance path so that current flows through it, as it has lower resistance than the rest of the current.

See Wikipedia's article on Shunt (electrical)

See Electrical 4 U site for the Shunt Resistor: What is it And How Does it Work?

And see, RS site for the article on A Guide to Shunt Resistors

For more information, please see Wikipedia's article on Ammeter.

Also, see Techie Scientist site for the article on Ammeter Vs Voltmeter: What’s The Difference

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What instrument is used to indicate high and low digital voltage states?

Logic probe.

See Electronics Notes for the article What is a Logic Probe?

Also, Techtown site for the article Logic Probe vs Multimeter: What are the Differences?

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What instrument may be used to verify proper radio antenna functioning?

An SWR meter.

From kd7bbc:

SWR = Standing Wave Ratio.

The Standing Wave Ratio is defined by wikipedia as the ratio of the partial standing wave's amplitude at an antinode (maximum) to the amplitude at a node (minimum) along the line.

Put in simpler terms, one of the most common ways to measure SWR is to use a directional wattmeter and measure the amount of power from the transmitter to the antenna (\(P_f\) = Forward power) as well as the amount of power coming back from the antenna to the transmitter (\(P_r\) = Reflected power).

The SWR can then be calculated using the formula:

\[\text{SWR} = \frac{1+\sqrt{P_r\over P_f}}{1-\sqrt{P_r\over P_f}}\]

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