Sheet 1

1-The current through a resistor is 1.5 A, but measurement yields a value of 1.46 A. compute the absolute
error and percentage of error of the measurement.

It= 1.5 A , Im= 1.46 A

eA=|It-Im|=|1.5-1.46|= 0.04 A
eA 0.04
eR = = =0.267
It 1.5
e%= eR *100 = 26.7 %

2-The value of a resistor is 2 KΩ; however, measurement yields a value of 1.93 KΩ. Compute the relative
and percentage accuracy of the measurement.

Rt= 2KΩ , Rm= 1.93KΩ

|Rt−Rm| |2−1.93|
A= 1- eR= 1- = 1- = 0.965
Rt 2
A%= A* 100= 96.5 %

3-If the average of a set of voltage readings is 30.15v. compute the precision of one of the readings that was
equal to 29.9 v

V= 30.15v, Vm=29.9 v
|30−29.9|
P= 1- = 0.997
30

4- The output voltage of an amplifier was measured by six different students using the same oscilloscope with
the following results 20.20 V, 19.90 V, 20.05 V, 20.10 V, 19.85 V, 20.00 V Which is the most precise
measurement?
20.20+19.90+ 20.05+20.10+19.85+20.00
V= = 20.0167 v
6
|V−Vi|
Pi=1-
V
The highest percision will have the least difference with the average |V-Vi|
Number 1 2 3 4 5 6
Volt 20.2 19.9 20.05 20.10 19.85 20
The difference 0.1833 0.1167 0.0333 0.0833 0.1667 0.0167

Therefore, the value 20 is the most precise.

5-Two resistors were selected from a supply of 2200±10% resistors.

(a) Assume both resistors are 2200± 0% Ω, compute the expected resistance of the parallel combination

R1=R2=2200
R//=R/2 = 1100 (no error)

(b) Assume both resistors are 2200+10% Ω, compute the expected resistance of the parallel
combination.what is the percent error when compared to a?

R1= R2 = 2200 * (1+0.1)= 2420

R//=R/2 = 1210
|1100−1210|
e%= * 100 = 10 %
1100

(c) Assume both resistors are 2200-10% Ω, compute the expected resistance of the parallel
combination.what is the percent error when compared to a?

R1=R2=2200*(1-0.1)= 1980
R//=R/2 = 990
|1100−990|
e%= * 100 = 10 %
1100

6-Three resistors, to be connected in series, were selected from a supply of 470.000±10% resistors.
(d) If all three resistors are 470.000± 0% Ω, what is the expected value of the series combination?
(e) If all three resistors are 470.000+10% Ω, what is the expected value of combination? what is the percent
error when compared to results in part a?
(f) If all three resistors are 470.000-10% Ω, what is the expected value of combination? what is the percent
error when compared to results in part a?

Similar to No 5

7- A 160 ± 10% pF capacitor, an inductor of 160±10% µH, and a resistor of 1200± 10%Ω are connected in
series
1
(a) If all three components are ±0%, and fr = /√𝐿𝐿𝐿𝐿, Compute the expected resonant frequency of the
2𝜋𝜋
combination
(b) If all three components are +10%, Compute the expected resonant frequency of the combination and
the percent error when compared to the results of part a.
(c) If all three components are -10%, Compute the expected resonant frequency of the combination and
the percent error when compared to results of part a

Similar to No 5

8- A 150 ± 10%Ω resistor is connected to terminals of a power supply operating at 200± 0 Vdc. What range
of the current would flow? If the resistor varies over the range of ±10% of its expected value? what is the
range of error in the current?
9- The diameter of a copper conductor varies over its length as shown in the following table.
(a) Calculate the precision of each measurement
(b) Calculate the average precision

Reading number Diameter (mm)

1 2.21
2 2.18
3 2.20
4 2.21
5 2.17
6 2.19

2.21+2.18+2.2+2.21+2.17+2.19
V= = 2.193 v
6

|V−Vi|
Pi=1-
V
0.992+0.994+0.997+0.992+0.989+0.999
P= = 0.9938
6

reading number Diamter (mm) Precision

1 2.21 0.992
2 2.18 0.994
3 2.20 0.997
4 2.21 0.992
5 2.17 0.989
6 2.19 0.999

10- A voltmeter is accurate to 98% of its full-scale reading.

(a) If a voltmeter reads 175 V on 300-V range. What is the absolute error of reading?

Here the accuracy is relative to the full scale not the true value
A= 1- (eA/range)
0.98=1- (eA/300)
eA= 6 volt

(b) What is the percentage of error of reading in part a?

As the voltmeter reads now, it means that the value that need to be read or the true value is
Vt=175 v. If voltmeter read means it is the measured value

e% = eA/Vt * 100 = 6/175 * 100 = 3.43%

11- Eight resistors having a color-coded value of 5.6KΩ were measured and found to have the following
values determine the standard deviation of the batch.

Resistor number Value (KΩ)

1 5.75
2 5.60
3 5.65
4 5.50
5 5.70
6 5.55
7 5.80
8 5.55

5.75+5.60+5.65+5.50+5.70+5.55+5.80+5.55
V= = 5.6375 v
8
di= Vi- V
Resistor number Value (KΏ) Deviation Di2
1 5.75 0.1125 0.01265625
2 5.60 -0.0375 0.00140625
3 5.65 0.0125 0.00015625
4 5.50 -0.1375 0.01890625
5 5.70 0.0625 0.00390625
6 5.55 -0.0875 0.00765625
7 5.80 0.1625 0.02640625
8 5.55 -0.0875 0.00765625

∑𝟖𝟖𝟏𝟏 𝒅𝒅𝒅𝒅𝟐𝟐
S= � = √(0.07875/8) = 0.0992
𝟖𝟖
12- A circuit was tuned for resonance by eight different students, and the following values for the resonant
frequency of the circuit were recorded. Compute the arithmetic mean, the average deviation, and the standard
deviation for reading.

Reading NO. Resonance frequency (kHz)

1 532
2 548
3 543
4 535
5 546
6 531
7 543
8 536

Similar to No 12