## RMS and Average Values of a Sine Wave

Alternating current flows periodically first in one direction and then in the opposite direction. One direction is called a positive alternation and the other direction is called a negative alternation. A complete positive and negative alternation is called one cycle. The number of complete cycles that occur each second is the frequency and is designated in hertz, abbreviated Hz. Therefore, if one complete cycle occurs per second, the frequency is 1 Hz; if 5 cycles are completed per second, the frequency is 5 Hz, and so on.

## Rectifier Meters

The moving-coil meter movement can only be used to measure dc, however; there is no way that it can be used to measure ac directly. If ac was applied directly to the meter, one half of the cycle would try to make the meter pointer move in one direction and the other half would try to make the pointer move in the opposite direction. Even at very low frequencies, the pointer would not be able to move fast enough to follow the positive and negative alternations of the ac wave. Therefore, instead of moving across the scale, the pointer would simply vibrate about zero. But, if the ac is first changed to DC before applying it to the meter movement then the moving-coil meter can be used in AC applications as well as DC.

Alternating current can be converted to DC by special devices called rectifiers. These devices offer a high opposition to current flow through them in one direction and a low opposition to current flow in the other direction. Therefore, when a sine wave is applied to a rectifier, it will pass either the positive alternation or the negative alternation, depending upon how the rectifier is connected into the meter circuit. In no case, however, will it pass both alternations. Therefore, a rectifier changes a sine wave to a pulsating dc wave. In a rectifier symbol, the arrow points in the direction of high resistance, so current flow through it is in the opposite direction. Rectifier meters use semiconductor rectifiers.

The Half-Wave Rectifier Meter

There are two basic types of rectifier circuits: the half-wave type and the full-wave type. In the half-wave type, one alternation of current passes through the meter movement and the opposite alternation is bypassed by the rectifier. Even though current through the meter is pulsating, the meter pointer, because of its inertia, will not have sufficient time to follow these fluctuations. Therefore, the meter pointer will rest at the average value of the current flowing through it.

The average current for one alternation is 0.637 of peak value, but, for the next alternation, it is zero and that alternation is bypassed by the meter. Therefore, the average current for a complete cycle is the sum of both alternations divided by 2, or 0.637/2 = 0.313 of the peak value. The meter pointer then deflects to the position on the scale that represents 0.318 of the peak value of the current flowing through the meter. But, for the reading to be meaningful the scale is usually calibrated to show the equivalent effective or RMS value. Therefore, the points on the scale are calibrated at 0.707 of the equivalent peak values.

References

http://www.eeeguide.com/ac-voltmeter-using-half-wave-rectifier/

https://circuitglobe.com/rectifier-type-instrument.html

https://www.electrical4u.com/rectifier-type-instrument-construction-principle-of-operation/

## Introduction to Electromagnetism

The Basic Meter

Meters, except for the few that operate on electromagnetic principles can only measure the amount of current flowing through them. However, they can be calibrated to indicate almost any electrical quantity. For example, you know that according to Ohm’s law, the current that flows through a meter is determined by the voltage applied to the meter and the resistance of the meter: I=        V/ R

## Calculating the Resistance of Multirange Multipliers

There are two methods of calculating the values of multiplier resistors for a multirange voltmeter. In the first method, each multiplier is calculated the same as for a single-range voltmeter. Assume that you wish to extend the range of a 1-mA movement to measure 0- 10, 0- 100, and 0- 1000 volts, and you also want a 0- 1-V range. Since full-scale deflection equals 1 Von the 0- 1-V range (V = IM RM = 0.001 A x 1000 Q = I volt), no multiplier is needed. The total resistance (RT OT) needed to limit meter current (IM) to 1 mA on the 0- 10-V range is RrnT = V w vJ IM   =   10 V/ 0.001A=    10,000 Q

## Current Tests: Part 1

Current tests are somewhat more difficult than voltage tests because although voltage tests are done while the circuit is energized, the test probes need only touch test points to get a voltage reading. Using the clamp-on ammeter is similarly easy since it needs simply to be clamped to the energized wire. With the in-line ammeter, though, a current test requires the power to be shut down, the circuit opened, the meter connected in place, the circuit closed again, and the power turned on to get a reading. There are similar steps when the test is completed and the wiring must be reconnected. Care must be taken in handling disconnected, loose wiring, and the ammeter must be firmly wired into the circuit with good resistance-free connections. Be sure the meter is firmly supported.

## Component Testers

The Wheatstone Bridge

When extremely accurate resistance measurements are required, a Wheatstone bridge is used. A Wheatstone bridge consists of four resistors connected in a diamond-shaped array. One of the resistors is the unknown one to be measured. A current source is connected to two opposite junctions and a sensitive meter is connected between the other two junctions. The meter has a zero-center reading.

To understand how a Wheatstone bridge measures resistance, assume that resistors R I and R2 each equal 400 ohms, and resistor R3 is variable from 0 to 1000 ohms. Now connect resistor Rx into the bridge circuit and close the switch. You can see that R1 and R3 form one divider network, and R2 and Rx form another divider network.  Therefore, since R1 equals R2, if R3 is made equal to Rx, the current and voltage drops in both dividers will be identical. Thus, the potentials at points C and D will be the same so that no current will flow through the meter. Therefore, when R3 is adjusted for a zero reading, you know its value equals that of Rx. The dial of variable resistor R3 is calibrated to show its exact resistance when adjusted. Therefore, its setting is also the value of unknown resistor Rx. Usually, the Wheatstone bridge contains many components so that different values of R 1, R2, and R3 can be switched in to test a wide range of resistances accurately.

Capacitors and Inductors

Prior to the development of the inexpensive digital meter, meters that measured capacitors and inductors were limited to expensive lab-type equipment. Today, though, many multimeters, as well as specialized meters, provide for routine testing of these components. Many digital volt-ohm-ammeters can check capacitors, with typical values from the low picofarads range to about 20 microfarads. Specialized test meters can test values up to 1 farad, as well as for capacitor leakage, equivalent series resistance, and dielectric absorption; some can also test inductors for values and for shorted turns.

The Wheatstone bridge can also be used to measure unknown values of capacitors and inductors in the same way as it does for resistors. However, since capacitors and inductors are reactive devices, an ac source must be used.

The same diamond-shaped array is used for the bridge, and a sensitive meter is connected between the same opposite junctions. The ac currents that are produced by the capacitive or inductive reactance’s in each leg will be the same when L3 or C3 equals Lx or Cx, as the case may be. This will cause points C and D to be at the same potential, and zero current will flow through the meter. The calibrated setting of L3 or C3 will show the value of Lx or Cx.

Diodes and Transistors

As explained for capacitors and inductors, the progress in digital meter design has allowed the meter to be used for a wide variety of sophisticated functions. In the past, analog multimeters were limited to testing resistive components; and then were able to handle capacitors and inductors. But these are all considered to be passive components with relatively fixed values. Active components, such as diodes and transistors, always required highly specialized test equipment.  They still do, for a complete and reliable analysis.

A few simple static tests can be made with diodes and transistors to give an initial idea of their reliability. With simple battery circuits and the diode connected with forward or reverse bias, the forward (high) current or the reverse (low) current can be measured. These quantities and the ratio of these quantities give an indication of the reliability of the diode.

Bipolar transistors are more difficult to check because of the complex characteristics and interaction among its three elements- the base, emitter, and collector.  Highly sophisticated equipment is needed to make complete dynamic tests. A typical digital multimeter, though, provides for testing the static forward current transfer ratio, which is the gain of the transistor in a circuit.

References

https://www.electronics-tutorials.ws/blog/wheatstone-bridge.html

http://www.seeedstudio.com/blog/2017/03/20/what-does-a-capacitor-do/

https://www.autodesk.com/products/eagle/blog/everything-need-know-capacitors/

## Analog Meters Introduction

Analog meters are so called because they do not measure the electrical characteristics directly. They do their measuring indirectly by measuring the effect of what is being measured. The effect and the amount of the effect are considered analogous to the original characteristic being measured. Usually, the current is the first characteristic tested and the effects of the current, either magnetic or thermal, are converted to movement with a deflected pointer. The greater the current being measured, the greater is the magnetic or thermal effect, and the greater the pointer deflection. The movement or distance of the pointer action, then, is analogous to the amount of current being measured.