0195136047.pdf

48 CIRCUIT CONCEPTS

Solution

When no instrument is connected, by voltage division,V+AG=1 V. With internal resistance

RVof the instrument, the voltmeter reading will be

VA= 2. 0

(

RV‖ 104

RV‖ 104 + 104

)

= 2

(

RV· 104

RV+ 104

)/(

RV· 104

RV+ 104

+ 104

)

= 2

RV· 104

2 × 104 RV+ 108

WithRV=1000,

VA=

2 × 107

2 × 107 + 108

=

2

2 + 10

=

2

12

= 0 .1667 V

for which the percent error is

1 − 0. 1667

1

× 100 = 83 .33%

WithRV= 107 ,

VA=

2 × 1011

2 × 1011 + 108

=

2000

2000 + 1

= 0 .9995 V

for which the percent error is

1 − 0. 9995

1

× 100 = 0 .05%

One can see why electronic voltmeters which have relatively very large internal resistance are

often used.

Ammeter

In order to measure the current through a wire or line of a circuit, an ammeter is connectedin

serieswith the line. A practical ammeter can usually be modeled as a series combination of an

ideal ammeter and an internal resistanceRI. The potential difference between the two terminals

of an ideal ammeter is zero, which corresponds to zero internal resistance. There are what are

known as dc ammeters and ac ammeters. An ac ammeter usually measures the rms value of the

time-varying current. Note that for the ammeter to be inserted for measuring current, the circuit

has to be broken, whereas for the voltmeter to be connected for measuring voltage, the circuit

need not be disassembled.

Multimetersthat measure multiple ranges of voltage and current are available in practice.

Ohmmetersmeasure the dc resistance by the use of Ohm’s law. A multimeter with scales for

volts, ohms, and milliamperes is known as VOM. An ohmmeter should not be used to measure

the resistance of an electronic component that might be damaged by the sensing current.

Instrument Transformers

These are generally of two types,potential transformers(PTs) andcurrent transformers(CTs).

They are designed in such a way that the former may be regarded as having an ideal potential

ratio, whereas the latter has an ideal current ratio. The accuracy of measurement is quite important

for ITs that are commonly used in ac circuits to supply instruments, protective relays, and control

devices.