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VOLTMETER.
• Peukur tegangan dipasang paralel
• Rm besar ( tahanan idaman ~ )
• Arus mengalir lewat peukur sangat kecil
V
10 kΩ 10 kΩ
5 kΩ 5 kΩ Rm = 3 k Ω10 V10 V
V V’ VBU = 10 V
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Tahanan pengali (multiplier).Dengan menambah sebuah atau beberapa tahanan secara seri dengan instrument dapat merobah batas ukur instrument tsb.
V = Im (Rs + Rm) Rs = (V-Im.Rm) / Im
Rs = (V/Im ) - Rm
Rm
ImGerakD’ Arsonval
RsI
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Multi range Voltmeter:
R1= (V1/Im) – Rm
R2= (V2/Im) – Rm
R3= (V3/Im) – Rm.
R1= (V1/Im) – Rm
R2= (V2/Im) – (Rm+R1)
R3=(V3/Im)–(Rm+R1+ R2)
R1
R3
R2
Rm
Im
V1
V2
V3 R3 R2 R1
V1
ImV2
V3
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PENGARUH PEROBAHAN TEMPERATUR
PADA VOLTMETER
Tahanan seri Rs tidak ter pengaruh perobahan suhu.
Rm terpengaruh dengan koefisien α pada (t2 – t1)
I = E / [Rm1+α(t2 – t1) + Rs]
= E / (Rm + Rs) x 1 – (α.Rm)/(Rm+Rs) x (t2 – t1)
Perubahan arus yang terjadi akibat perubahan temperatur:
(α.Rm) / (Rm+Rs) x (t2 – t1) x 100%
E
RsI
Rm
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Contoh :Voltmeter dengan Rs = 45 Ω Rm= 5 Ω masing2
terbuat dari bahan manganin dan tembaga. Koefisien temperatur Rs = 0 %/oC dan α untuk Rm = 0,4 %/oC pada perobahan dari 20 oC ke 30 oCPenyelesaian: Perubahan arus yang terjadi:
(α.Rm) / (Rm+Rs) x (t2 – t1) x 100%(0,004x5) / (45+5) x10 x100% = 0,4 %Terjadi kesalahan baca akibat perobahan arus mengalir sebesar 0,4 %
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SENSITIFITAS
Input resistan dari voltmeter yang paling simpel adalah: Rin = Rs + Rm atau
Rin = V / Im
Faktor sensitivitas =>
S di defenisikan 1/arus skala penuh.
S = 1/Im atau S = 1/ A
= 1 / V/ Ω = Ω / V
Rm = S x V
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LOADING EFFECT
Va-b = (200 / 200 + 200)x 100 V = 50 V
Va-b (terukur Voltmeter dgn S = 20 kΩ/V) :
mempunyai => Rin = S x V = 20 kΩ/V x 50 V => 1000 kΩ
kemudian : Rin // R2 = (200x1000)/1200 = 200.000 / 1.200
= 166,667 kΩ.
Va-b = 166,667/(200 + 166,667) x`100 V = 45,45 V
Teg sesungguhnya 50 V, terbaca : 45,45 V.
LOADING EFFECT => penyusutan tegangan terukur dari
tegangan sesungguhnya.
V
200 kΩ
200 kΩ100 VS=20 k Ω / V
R1
R2
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AKURASI:
Kv = Vw / Vo ;
I = Vo / (Ro + Rin)
Vw = teg terukur
Vo = teg sesungguhnya
Tegangan terukur :
Vw = I. Rin atau Vw = Rin/(Ro+Rin) x Vo
Jadi Kv = Vw / Vo
Kv = Rin / (Ro + Rin)
LOADING ERROR :
Loading Error (%) = (1 – Kv) 100
Ro
VIVoVw
Rin = Rs+Rm
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Contoh:
Vo = (200 / 200 + 200)x 100 V = 50 V Ro ( Requvalen bila dilihat dari a-b) =>
Ro = (200x200)/(200+200) = 100 kΩ
Rin = S . V = 20 kΩ/V x 50 V => 1000 kΩVw = Rin / (Ro + Rin) x Vo => Vw = 103 / (100+ 103) x 50V =>Vw = 45,45 Volt
Kv = Vw/Vo = 45,45/50 x 100%Kv = 91 %.
V
200 kΩ100 VS=20 k Ω / V
R1
R2
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10
Example 5.4 A voltmeter with sensitivity of 20kΩ/V is used for measuring a voltage across R2 with range of 50V as shown in figure below. Calculate
a) reading voltage
b) accuracy of measurement
c) error of measurement
Solution
inThTh RRV ,,Find
kkkRRR
kkk
V
RRR
EVV
Th
womTh
100200//200//
50200200200
100
21
221
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11
MVV
kRangeSRin 150
20
wmVvoltage,readingFind
VVkM
M
VRR
RV wom
Thin
inwm
45.45501001
1
VMkM
V
RRR
VV in
Thin
Thwm
45.4511001
50
or
tmeasuremenofaccuracyFind
909.05045.45VV
V
VAccuracy
wom
wm
909.02001
1
or
kMM
RR
RAccuracy
Thin
in
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12
tmeasuremenoferrorFind
091.050
45.4550or
091.0909.011
VVV
X
XXError
AccError
t
mt
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