Physics and Engineering of Radiation Detection

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Appendix A

Essential Electronic Measuring Devices

A.1 Multimeters................................

Multimeter is a general purpose device used to measure voltage, current, and impedance.

Some multimeters are also equipped with capacitance measuring circuitry. There

are essentially two kinds of multimeters: analog and digital. Before we go into their

descriptions, it is worthwhile to discuss what is actually meant by measuring voltage

and current.

A.1.A MeasuringVoltageandCurrent.................

The information carried by a signal is contained in its power given by

P = VI

⇒P =

V^2

R

or P∝V^2 ,

and similarly P = I^2 R or P∝I^2.

This implies that the relevant quantity for measurement is actually the average

of thesquaredvoltage or current and not the simple average. In fact, if we take

an example of a simple pure sinusoidal wave and take its average, the result will

be 0. The simple average is therefore not a good measure of the power information

contained in the signal. Therefore the multimeters actually measure the average of

the squared voltage and current. This quantity is known as the root mean square

value and is defined for periodic and continuous voltage and current by

Vrms =

[

1

T

∫T

0

(V(t))^2 dt

] 1 / 2

(A.1.1)

Irms =

[

1

T

∫T

0

(I(t))^2 dt

] 1 / 2

, (A.1.2)

whereT=1/fis the period (peak-to-peak time) of the signal having frequencyf.

To get a feeling of therms-voltage with respect to the peak voltage, let us look

at the example of a pure sinusoidal wave given by

V(t)=V 0 sin(2πft), (A.1.3)

whereV 0 is the peak voltage or amplitude of the signal. Using the above relation,

the root mean square voltage is

Vrms=0. 707 V 0. (A.1.4)