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

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Electrical and Electronic Measuremen ts:
Measuremen t & Resistance F orm ula Sheet for
Electrical GA TE
Error Analysis in Resistance Measuremen t
• Absolute Error : Difference b et w een measured and true resistance.
E = R
m
-R
t
where R
m
is measured resista nce, R
t
is true resistance (? ).
• Relativ e Error : Ratio of absolute error to true resistance.
Relativ e Error=
E
R
t
• P ercen tage Error : Relativ e error expressed as a p ercen tage.
P ercen tage Error=
E
R
t
×100
• Limiting Error : Maxim um p ossible error based on instrumen t accuracy .
Limiting Error=± F ull Scale V alue× A ccuracy
Resistance Measuremen t Metho ds
• Ohm’s La w Metho d : Resistance from v oltage and curren t.
R =
V
I
where V is v oltage (V ), I is curren t (A ), R is resistance (? ).
• V oltmeter-Ammeter Metho d : Resistance measuremen t with corrections for meter
errors.
R =
V
measured
I
measured
A ccoun t for v oltmeter resistance (R
v
) and ammeter resistance (R
a
).
• Wheatstone Bridge : F or medium resistance measuremen t (1 ? to 1 M? ).
R
1
R
2
=
R
3
R
x
Unkno wn resistance:
R
x
= R
3
·
R
2
R
1
where R
1
,R
2
,R
3
are kno wn resistances, R
x
is unkno wn resistance.
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Electrical and Electronic Measuremen ts:
Measuremen t & Resistance F orm ula Sheet for
Electrical GA TE
Error Analysis in Resistance Measuremen t
• Absolute Error : Difference b et w een measured and true resistance.
E = R
m
-R
t
where R
m
is measured resista nce, R
t
is true resistance (? ).
• Relativ e Error : Ratio of absolute error to true resistance.
Relativ e Error=
E
R
t
• P ercen tage Error : Relativ e error expressed as a p ercen tage.
P ercen tage Error=
E
R
t
×100
• Limiting Error : Maxim um p ossible error based on instrumen t accuracy .
Limiting Error=± F ull Scale V alue× A ccuracy
Resistance Measuremen t Metho ds
• Ohm’s La w Metho d : Resistance from v oltage and curren t.
R =
V
I
where V is v oltage (V ), I is curren t (A ), R is resistance (? ).
• V oltmeter-Ammeter Metho d : Resistance measuremen t with corrections for meter
errors.
R =
V
measured
I
measured
A ccoun t for v oltmeter resistance (R
v
) and ammeter resistance (R
a
).
• Wheatstone Bridge : F or medium resistance measuremen t (1 ? to 1 M? ).
R
1
R
2
=
R
3
R
x
Unkno wn resistance:
R
x
= R
3
·
R
2
R
1
where R
1
,R
2
,R
3
are kno wn resistances, R
x
is unkno wn resistance.
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• Kelvin Bridge : F or lo w resistance measuremen t (< 1 ? ).
R
x
= R
s
·
R
2
R
1
where R
s
is standard lo w resistance, accoun ts for lead and con tact resistances.
• Loss of Charge Metho d : F or high resistance measuremen t (> 1 M? ).
R =
t
Cln
(
V
1
V
2
)
where t is time (s ), C is capacitance (F ), V
1
,V
2
are initial and final v oltages.
P oten t iometer for Resistance Measuremen t
• DC P oten tiometer : Compares unkno wn resistance via v oltage drop.
R
x
= R
s
·
l
x
l
s
where R
s
is standard resistance, l
x
,l
s
are lengths of p oten tiometer wire for unkno wn
and standard resistances.
T e mp e rature Effects on Resistance
• Resistance V ariation with T emp erature :
R
t
= R
0
[1+a(T -T
0
)]
where R
t
is resistance at temp erature T , R
0
is resistance at re ference temp erature T
0
,
a is temp erature co e?icien t of resistance ( K
-1
).
Key Notes
• Standard units: Resistance (? ), V oltage (V ), Curren t (A ), Capacitance (F ), Time (s ).
• Wheatstone bridge is balanced when no curren t flo ws through the galv anometer.
• Kelvin bridge corrects for lead/con tact resistance in lo w resistance measuremen ts.
• F or high resistance, use sensitiv e instrumen ts lik e electrometers.
• Use SI units for GA TE calculations.
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