Formula Sheets: Measurements & Measuring Systems | Electrical and Electronic Measurements - Electrical Engineering (EE) PDF Download

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Electrical and Electronic Measuremen ts:
Measuremen ts & Measuring Systems F orm ula Sheet
for Electrical GA TE
Error Analysis
• Absolute Error : Difference b et w een measured and true v alue.
E =X
m
-X
t
where X
m
is measur ed v alue, X
t
is true v alue.
• Relativ e Error : Ratio of absolute error to true v alue.
Relativ e Error=
E
X
t
• P ercen tage Error : Relativ e error expressed as a p ercen tage.
P ercen tage Error=
E
X
t
×100
• Limiting Error : Maxim um p ossible error in a measuremen t.
Limiting Error=± F ull Scale V alue× A ccuracy
DC Bridges
• Wheatstone Bridge : Condition for balance.
R
1
R
2
=
R
3
R
4
where R
1
,R
2
,R
3
,R
4
are bridge arm resistances.
• Unkno wn Resistance : Using Wheatstone bridge balance.
R
x
=R
s
·
R
2
R
1
where R
x
is unkno wn resistance, R
s
is standard resistance.
• Kelvin Bridge : F or lo w resistance measuremen t.
R
x
=R
s
·
R
2
R
1
(A ccoun ts for lead resistance, similar balance condition).
1
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Electrical and Electronic Measuremen ts:
Measuremen ts & Measuring Systems F orm ula Sheet
for Electrical GA TE
Error Analysis
• Absolute Error : Difference b et w een measured and true v alue.
E =X
m
-X
t
where X
m
is measur ed v alue, X
t
is true v alue.
• Relativ e Error : Ratio of absolute error to true v alue.
Relativ e Error=
E
X
t
• P ercen tage Error : Relativ e error expressed as a p ercen tage.
P ercen tage Error=
E
X
t
×100
• Limiting Error : Maxim um p ossible error in a measuremen t.
Limiting Error=± F ull Scale V alue× A ccuracy
DC Bridges
• Wheatstone Bridge : Condition for balance.
R
1
R
2
=
R
3
R
4
where R
1
,R
2
,R
3
,R
4
are bridge arm resistances.
• Unkno wn Resistance : Using Wheatstone bridge balance.
R
x
=R
s
·
R
2
R
1
where R
x
is unkno wn resistance, R
s
is standard resistance.
• Kelvin Bridge : F or lo w resistance measuremen t.
R
x
=R
s
·
R
2
R
1
(A ccoun ts for lead resistance, similar balance condition).
1
A C Bridges
• General A C Bridge Balance : Imp edance balance condition.
Z
1
Z
4
=Z
2
Z
3
where Z
1
,Z
2
,Z
3
,Z
4
are complex imp edance s.
• Maxw ell’s Bridge : F or inductance measuremen t.
L
x
=R
2
R
3
C
4
, R
x
=
R
2
R
3
R
4
whereL
x
is unkno wn inductance,R
x
is unkno wn resistance,C
4
is kno wn capacitance.
• Sc hering Bridge : F or capacitance measuremen t.
C
x
=C
s
·
R
4
R
3
, Dissipation F actor=?C
s
R
s
whereC
x
is unkno wn capacitance,C
s
is standard capacitance,? is angular frequency .
• Wien Bridge : F or frequency measuremen t.
f =
1
2p
v
R
1
R
2
C
1
C
2
Measuring Instrumen ts
• PMMC Instrumen t : Deflection torque.
T
d
=NBIA
where T
d
is deflection torque, N is n um b er of turns, B is magnetic flux densit y , I is
curren t, A is coil area.
• Mo ving Iron Instrumen t : T orque prop ortional to square of curren t.
T
d
?I
2
• Electro dynamometer : F or p o w er measuremen t.
P =VIcos?
where ? is phase angle b et w een v oltage and curren t.
• Energy Meter : Energy consumed.
E =P ·t
where E is energy (Wh ), P is p o w er (W ), t is time (h ).
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Page 3


Electrical and Electronic Measuremen ts:
Measuremen ts & Measuring Systems F orm ula Sheet
for Electrical GA TE
Error Analysis
• Absolute Error : Difference b et w een measured and true v alue.
E =X
m
-X
t
where X
m
is measur ed v alue, X
t
is true v alue.
• Relativ e Error : Ratio of absolute error to true v alue.
Relativ e Error=
E
X
t
• P ercen tage Error : Relativ e error expressed as a p ercen tage.
P ercen tage Error=
E
X
t
×100
• Limiting Error : Maxim um p ossible error in a measuremen t.
Limiting Error=± F ull Scale V alue× A ccuracy
DC Bridges
• Wheatstone Bridge : Condition for balance.
R
1
R
2
=
R
3
R
4
where R
1
,R
2
,R
3
,R
4
are bridge arm resistances.
• Unkno wn Resistance : Using Wheatstone bridge balance.
R
x
=R
s
·
R
2
R
1
where R
x
is unkno wn resistance, R
s
is standard resistance.
• Kelvin Bridge : F or lo w resistance measuremen t.
R
x
=R
s
·
R
2
R
1
(A ccoun ts for lead resistance, similar balance condition).
1
A C Bridges
• General A C Bridge Balance : Imp edance balance condition.
Z
1
Z
4
=Z
2
Z
3
where Z
1
,Z
2
,Z
3
,Z
4
are complex imp edance s.
• Maxw ell’s Bridge : F or inductance measuremen t.
L
x
=R
2
R
3
C
4
, R
x
=
R
2
R
3
R
4
whereL
x
is unkno wn inductance,R
x
is unkno wn resistance,C
4
is kno wn capacitance.
• Sc hering Bridge : F or capacitance measuremen t.
C
x
=C
s
·
R
4
R
3
, Dissipation F actor=?C
s
R
s
whereC
x
is unkno wn capacitance,C
s
is standard capacitance,? is angular frequency .
• Wien Bridge : F or frequency measuremen t.
f =
1
2p
v
R
1
R
2
C
1
C
2
Measuring Instrumen ts
• PMMC Instrumen t : Deflection torque.
T
d
=NBIA
where T
d
is deflection torque, N is n um b er of turns, B is magnetic flux densit y , I is
curren t, A is coil area.
• Mo ving Iron Instrumen t : T orque prop ortional to square of curren t.
T
d
?I
2
• Electro dynamometer : F or p o w er measuremen t.
P =VIcos?
where ? is phase angle b et w een v oltage and curren t.
• Energy Meter : Energy consumed.
E =P ·t
where E is energy (Wh ), P is p o w er (W ), t is time (h ).
2
Instrumen t T ransformers
• Curren t T ransformer (CT) : Curren t ratio.
I
p
I
s
=
N
s
N
p
where I
p
,I
s
are primary and secondary curren ts, N
p
,N
s
are primary and secondary
turns.
• P oten tial T ransformer (PT) : V oltage ratio.
V
p
V
s
=
N
p
N
s
where V
p
,V
s
are primary and se condary v oltages.
Key Notes
• Standard units: V oltage (V ), Curren t (A ), Resistance (? ), Capacitance (F ), Induc-
tance (H ), P o w er (W ), F requency (Hz ).
• F or bridges, ensure balance condition is satisfied b efore applying form ulas.
• PMMC is used for DC, Mo ving Iron for b oth A C/DC, Electro dynamomet er for precise
A C measuremen ts.
• Use SI units for GA TE calculations.
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