Resistance Measurement

• Most Often Used Methods– Ampermeter and Voltmeter Method– Whetstone Bridge Method

A-m and V-m Method

• Easy to perform,

• Easy to calculate the resistance,

• Easy to calculate the measurement error,

• Accuracy depend on the accuracy of instrumentation,

• Resistance of contacts influences the results,

Two A-m V-m Methods

• V-m Connected in Front of A-m,• A-m Connected in Front of V-m

• Which method to use when???

A

V RxVs

A

V RxVs

V-m Connected in Front of A-m

A

V Rx

IIa

Iv

Rv

Ra

Vv VxVs

Calculation

• Approximate Value of Unknown Resistance

a

vx I

VR '

Calculation

a

x

x

xx I

V

I

VR

Where Vx is:

Exact Value of Unknown Resistance

aavx IRVV

Calculation

aa

vx RI

VR

axx RRR '

Absolute Error

axx RRRA '

00 ARa

Percentage Error

%100v

aa

V

IRR

%100%100 '' x

a

x R

R

R

AR

Percentage Error

0' RRx

This methods is used forlarger resistance!

Example 1:

mAI

VV

R

kR

a

v

a

v

2

2.10

1

100

Example 1 Calculation:

51002

2.10'

mA

V

I

VR

a

vx

Approximate Value of Unknown Resistance:

Exact Value of Unknown Resistance:

5099

15100'

x

axx

R

RRR

Example 1 Error Calculation

1'xx RRA

Absolute Error:

%02.0

%1005100

1%100'

R

RxR

A

Percentage Error:

Example 2

1.5'xR

If we use the same circuit to measure unknownapproximate resistance of:

Percentage error would be:

%6.19R

A-m Connected in Front of V-m

A

V Rx

Ia Ix

Iv

Rv

Ra Vv

VxVs

Calculation

• Approximate Value of Unknown Resistance

a

vx I

VR '

Calculation

x

v

x

xx I

V

I

VR

Where Ix is:

Exact Value of Unknown Resistance

vax III

Calculation

va

v

xa

vx

RV

I

V

II

VR

Absolute Error

v

va

v

a

v

xx

RV

I

V

I

VA

RRA

'

0 ARv

Percentage Error

%100v

aa

V

IRR %100

%100'

a

v

v

va

v

a

v

x

IV

RV

I

VIV

R

R

AR

Percentage Error

00' RRx

This methods is used forsmaller resistance!

Example 3:

AI

VV

R

kR

x

v

a

v

2

2.10

1

100

Example 3 Calculation:

1.52

2.10'

A

V

I

VR

x

vx

Approximate and Exact Value of Unknown Resistance:

1005.5

502.10

2

2.10

kV

A

V

RV

I

VR

v

va

vx

Example 3 Error Calculation

00052.0'xx RRA

Absolute Error:

%01.0

%1001.5

00052.0%100'

R

RxR

A

Percentage Error:

Example 4

5100'xR

If we use the same circuit to measure unknownapproximate resistance of:

Percentage error would be:

%3.11R

CONCLUSION

• V-m in front of A-m - for LARGER “R”

• A-m in front of V-m - for SMALLER “R”