Formula Sheets: Electromechanical Indicating Instruments | Electrical and Electronic Measurements - Electrical Engineering (EE) PDF Download

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Electrical and Electronic Measuremen ts:
Electromec hanical Indicating Instrumen ts F orm ula
Sheet for Electrical GA TE
P ermanen t Magnet Mo ving Coil (PMMC) Instrumen ts
• Deflection T orque : T orque causing coil deflection in a magnetic field.
T
d
=NBIA
where T
d
is deflection torque ( Nm ), N is n um b er of coil turns, B is magnetic flux
densit y (T ), I is curren t (A ), A is coil area (m
2
).
• Con trolling T orque : Pro vided b y springs to opp ose deflection.
T
c
=k?
where T
c
is con trolling torque (Nm ), k is spring constan t (Nmrad
-1
), ? is deflection
angle (rad ).
• Equilibrium Deflection : A t balance, T
d
=T
c
.
?=
NBIA
k
(Deflection is prop ortional to curren t, making PMMC suitable for DC measuremen ts).
• Sh un t Resistance for Ammeter : Extends curren t range.
R
sh
=
R
m
m-1
where R
sh
is sh un t resistance (? ), R
m
is meter resistance, m =
I
Im
(curren t m ultipli-
cation factor).
• Series Resistance for V oltmeter : Extends v oltage range.
R
se
=
V
I
m
-R
m
whereR
se
is series resistance (? ),V is desired v oltage range (V ),I
m
is full-scale meter
curren t.
Mo ving Iron (MI) Instrumen ts
• Deflection T orque : Prop ortional to square of curren t.
T
d
?I
2
(Suitable for b oth A C and DC measuremen ts).
• Con trolling T orque : Pro vided b y springs.
T
c
=k?
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Electrical and Electronic Measuremen ts:
Electromec hanical Indicating Instrumen ts F orm ula
Sheet for Electrical GA TE
P ermanen t Magnet Mo ving Coil (PMMC) Instrumen ts
• Deflection T orque : T orque causing coil deflection in a magnetic field.
T
d
=NBIA
where T
d
is deflection torque ( Nm ), N is n um b er of coil turns, B is magnetic flux
densit y (T ), I is curren t (A ), A is coil area (m
2
).
• Con trolling T orque : Pro vided b y springs to opp ose deflection.
T
c
=k?
where T
c
is con trolling torque (Nm ), k is spring constan t (Nmrad
-1
), ? is deflection
angle (rad ).
• Equilibrium Deflection : A t balance, T
d
=T
c
.
?=
NBIA
k
(Deflection is prop ortional to curren t, making PMMC suitable for DC measuremen ts).
• Sh un t Resistance for Ammeter : Extends curren t range.
R
sh
=
R
m
m-1
where R
sh
is sh un t resistance (? ), R
m
is meter resistance, m =
I
Im
(curren t m ultipli-
cation factor).
• Series Resistance for V oltmeter : Extends v oltage range.
R
se
=
V
I
m
-R
m
whereR
se
is series resistance (? ),V is desired v oltage range (V ),I
m
is full-scale meter
curren t.
Mo ving Iron (MI) Instrumen ts
• Deflection T orque : Prop ortional to square of curren t.
T
d
?I
2
(Suitable for b oth A C and DC measuremen ts).
• Con trolling T orque : Pro vided b y springs.
T
c
=k?
1
• Equilibrium Deflection : A t balance, deflection prop ortional to I
2
.
??I
2
• A ttraction T yp e : F orce on iron piece in magnetic field.
F ?
I
2
d
2
where d is distance b et w een iron piece a nd coil.
Electro dynamometer Instrumen ts
• Deflection T orque : Prop ortional to pro duct of curren ts in fixed and mo ving coils.
T
d
=kI
1
I
2
where I
1
,I
2
are curren ts in fixed and mo ving coils ( A ), k is a c onstan t.
• P o w er Measuremen t : F or w attmeter applications.
P =VIcos?
where P is p o w er (W ), V is v oltage (V ), I is curren t, ? is phase angle.
• Deflection for W attmeter :
??VIcos?
(Suitable for A C p o w er measuremen ts, can b e used for DC).
Electrostatic Instrumen ts
• Deflection T orque : Prop ortional to square of v oltage.
T
d
=
1
2
?A
V
2
d
2
where ? is p ermittivit y , A is plate area (m
2
), V is v oltage (V ), d is plate separation
(m ).
• Equilibrium Deflection :
??V
2
(Used for high-v oltage A C/DC measuremen ts).
Key Notes
• Standard units: Curren t (A ), V oltage (V ), Resistance (? ), P o w er (W ), T orque (Nm ).
• PMMC: DC only , linear scale. MI: A C/DC, non-linear scale. Electro dynamometer:
A C/DC, precise for p o w er. Electrostatic: High-v oltage A C/DC.
• Sh un t/series resistances m ust accoun t for meter’s in ternal resistance.
• Damping (air or eddy curren t) ensures steady deflection.
• Use SI units for GA TE calculations.
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