Formula Sheets: Measuring Instruments | Basic Electrical Technology - Electrical Engineering (EE) PDF Download

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Basic Electrica l T ec hnology: Measuring Instrumen ts
F orm ula Sheet for Electrical GA TE
Ammeters and V oltmeters
• Ammeter Sh un t Resistance :
R
sh
=
R
m
I
m
I-I
m
where R
sh
is sh un t resistance (? ), R
m
is meter resistance (? ), I
m
is full-scale meter
curren t (A ), I is total curren t to b e measured.
• V oltmeter Series Resistance :
R
se
=
V
I
m
-R
m
where R
se
is series resistance (? ), V is v oltage to b e measured (V ).
• Sensitivit y of V oltmeter :
S =
1
I
fs
(?V
-1
)
where I
fs
is full-scale curre n t of the meter.
• Loading Effect (V oltmeter) :
V
actual
=V
source
·
R
v oltmeter
R
source
+R
v oltmeter
W attmeters
• P o w er Measured b y W attmeter :
P =VIcos?
where P is p o w er (W ), V is RMS v oltage (V ), I is RMS curren t (A ), cos? is p o w er
factor.
• T w o-W attmeter Metho d (Three-Phase) :
P
total
=P
1
+P
2
tan?=
v
3
P
1
-P
2
P
1
+P
2
where P
1
, P
2
are readings of the t w o w attmeters.
Energy Meters
• Energy Measured :
E =P ·t
where E is energy (Wh or kWh ), P is p o w er (W ), t is time (h ).
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Basic Electrica l T ec hnology: Measuring Instrumen ts
F orm ula Sheet for Electrical GA TE
Ammeters and V oltmeters
• Ammeter Sh un t Resistance :
R
sh
=
R
m
I
m
I-I
m
where R
sh
is sh un t resistance (? ), R
m
is meter resistance (? ), I
m
is full-scale meter
curren t (A ), I is total curren t to b e measured.
• V oltmeter Series Resistance :
R
se
=
V
I
m
-R
m
where R
se
is series resistance (? ), V is v oltage to b e measured (V ).
• Sensitivit y of V oltmeter :
S =
1
I
fs
(?V
-1
)
where I
fs
is full-scale curre n t of the meter.
• Loading Effect (V oltmeter) :
V
actual
=V
source
·
R
v oltmeter
R
source
+R
v oltmeter
W attmeters
• P o w er Measured b y W attmeter :
P =VIcos?
where P is p o w er (W ), V is RMS v oltage (V ), I is RMS curren t (A ), cos? is p o w er
factor.
• T w o-W attmeter Metho d (Three-Phase) :
P
total
=P
1
+P
2
tan?=
v
3
P
1
-P
2
P
1
+P
2
where P
1
, P
2
are readings of the t w o w attmeters.
Energy Meters
• Energy Measured :
E =P ·t
where E is energy (Wh or kWh ), P is p o w er (W ), t is time (h ).
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• Meter Constan t :
K =
Num b er of rev olutions
Energy in kWh
(kW
-1
h)
• Energy Calculation :
E =
Num b er of rev olutions
K
Errors in Measuremen ts
• P ercen tage Error :
% Error=
Measured V alue- T rue V alue
T rue V alue
×100
• Relativ e Error :
Relativ e Error=
Absolute Error
T rue V alue
• Instrumen t Error (Ammeter/V oltmeter) :
% Error=
I
m
R
m
I
×100 (Ammeter), % Error=
V
V
fs
×100 (V oltmeter)
where V
fs
is full-scale v oltage.
Bridge Measuremen ts
• Wheatstone Bridge (Balanced Condition) :
R
1
R
2
=
R
3
R
4
where R
1
,R
2
,R
3
,R
4
are bridge resistances (? ).
• Unkno wn Resistance :
R
x
=R
std
·
R
2
R
1
where R
x
is unkno wn resistance, R
std
is standard resistance.
Key Notes
• Ammeter : Lo w resistance, connected in series; sh un t extends range.
• V oltmeter : High resistance, connected in parallel; series resistor extends range.
• T w o-W attmeter Metho d : V alid for balanced/un balanced three-phase loads; p o w er
factor calculation critical.
• GA TE F o cus : Calculate sh un t/series resistances, errors, and p o w er factor from
w attmeter readings.
• Units : Use SI units for GA TE (e.g., V , A , W , ? , kWh ).
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