Electrical Measurements & Instrumentation

Course Code: EEE 374

Lecture 9
Course Instructor: Dr. Hammad Omer (Assistant Professor)
(PhD, MS, MCS, PGD (IT) B.Eng.)
Commonwealth Scholar (Imperial College London, United Kingdom)
Group Lead: Medical Image Processing Research Group
(www.miprg.com)
Department of Electrical Engineering
COMSATS University, Islamabad
Dated: 24 October 2024
1
 Series Ohmmeter
• An ohmmeter is normally part of a volt-ohm-milliammeter (VOM), or
multimeter function
• Ohmmeters do not usually exist as individual instruments
• The simplest ohmmeter circuit consists of a voltage source
connected in series with a pair of terminals, a standard resistance
and a low-current PMMC instrument
• The resistance to be measured (Rx) is connected across terminals A
and B
• The meter current indicated by the instrument (in Figure 3.21) is:
battery voltage/total series resistance:
𝐸𝑏
𝐼𝑚 =
𝑅𝑥 +𝑅1 +𝑅𝑚
• When the external resistance is zero (i.e. terminals A and B short-
circuited), the above equation becomes:
𝐸𝑏
𝐼𝑚 =
𝑅1 + 𝑅𝑚
2
Series Ohmmeter

3
 Series Ohmmeter
• If R1 and Rm are selected (or if R1 is adjusted) to give FSD when A
and B are short circuited, FSD is marked as zero ohms
• Therefore, for Rx=0, the pointer indicates 0Ω
• When terminals A and B are open-circuited, the effective value of
resistance Rx is infinity; no meter current flows and the pointer
indicates zero current; this point is marked as infinity on the
resistance scale
• If a resistance Rx with a value between zero and infinity is connected
across terminals A and B, the meter current is greater than zero but
less than FSD
• The pointer position on the scale depends on the relationship
between Rx and R1+Rm (as seen in the next example)
• In the next question; it is observed that the measured resistance at
center scale is equal to the internal resistance of the ohmmeter
(Rx=R1+Rm); because at FSD the total resistance is R1+Rm and when
the resistance is doubled (Rx+R1+Rm=2(R1+Rm)), the circuit current is
halved 4
Series Ohmmeter (Question)

5
Series Ohmmeter (Question)

6
Series Ohmmeter (Question)

7
 Ohmmeter with Zero Adjust
• The simple Ohmmeter discussed above will operate satisfactorily as
long as the battery voltage remains exactly at 1.5V
• When the battery voltage falls (and the output voltage of all batteries
fall with use) the instrument scale is no longer correct
• Even if R1 were adjusted to give FSD when terminals A and B are
short circuited, the scale would still be in error because now midscale
would represent a resistance equal to new value of R1+Rm
• Falling battery voltage can be taken care of by an adjustable resistor
connected in parallel with the meter (R2 in Figure 3.22)
• In the modified circuit, the battery current Ib splits into meter current
Im and resistor current I2
• With terminals A and B short circuited, R2 is adjusted to give FSD on
the meter
• At this time, the total circuit resistance is R1+R2||Rm
• Since R1 is always very much larger than R2||Rm, the total resistance
can be assumed to equal R1
8
Ohmmeter with Zero Adjust

9
 Ohmmeter with Zero Adjust
• When a resistance Rx equal to R1 is connected across terminals A
and B, the circuit resistance is doubled and the circuit current is
halved
• This causes both I2 and Im to be reduced to half of their previous
levels (i.e. when A and B were short-circuited)
• Thus, the midscale measured resistance is again equal to the
ohmmeter internal resistance R1
• The equation for the battery current in Figure 3.22 is:
𝐸𝑏
𝐼𝑏 =
𝑅𝑥 +𝑅1 +𝑅2 ||𝑅𝑚
𝐸𝑏
• If R2||Rm <<R1: 𝐼𝑏 ≅
𝑅𝑥 +𝑅1
• Also, the meter voltage is: 𝑉𝑚 = 𝐼𝑏 (𝑅2 ||𝑅𝑚 )
𝐼𝑏(𝑅2 ||𝑅𝑚 )
• Which gives the meter current as: 𝐼𝑚 =
𝑅𝑚

10
 Ohmmeter with Zero Adjust
• Each time the Ohmmeter is used, terminals A and B are first short-
circuited, and R2 is adjusted for zero-ohm indication on the scale (i.e.
for FSD)
• If this procedure is followed, then even when the battery voltage falls
below its initial level, the scale remains correct

11
Ohmmeter with Zero Adjust (Question)

12
Ohmmeter with Zero Adjust (Question)

13
Ohmmeter with Zero Adjust (Question)

14
Ohmmeter with Zero Adjust (Question)

15
Series Ohmmeter (Question)

16
17