UNIVERSITY OF ENGINEERING AND TECHNOLOGY
PESHAWAR, ABBOTTABAD CAMPUS
COMPLEX ENGINEERING PROBLEM
(CEP)
COURSE TITLE: INSTRUMENTATION AND MEASUREMENTS
COURSE NO: ELE-250
SUBMITTED TO: ENGR. MUHAMMAD AYAZ
SUBMITTED BY: MALEEHA NASEER
REG. NO: 22ABELT0937
CLASS NO: 11
DATE OF SUBMISSION: 10-JANUARY-2025
1
CEP Statement:
Implement the given task using Multisim or LabView software. Ensure to calculate all
required values manually and compare these with the results obtained from simulations.
Task:
A PMMC (Permanent Magnet Moving Coil) instrument is equipped with a three-resistor
Ayrton shunt to function as an ammeter, as shown in Figure 1 below. The meter has an
internal resistance Rm = 1 kΩ and a full-scale deflection (FSD) of 100 µA. To measure the
current in a circuit consisting of variable resistance (5 kΩ to 20 kΩ) and a voltage source of
100 V.
Calculate the values of the resistors (Ω) for the Ayrton shunt configuration.
Figure 1: Multirange ammeter circuit Calculations:
Values given,
Meter resistance, 𝑅𝑚 = 1𝑘Ω
Full-scale deflection (FSD), 𝐼𝑚 = 100 µA
Variable resistance, 5 kΩ to 20 kΩ
Voltage source, 𝑉𝑠 = 100 V
As, 𝑉𝑠 = 𝑉𝑚 = 𝐼𝑚𝑅𝑚
𝑉𝑚 = 100 µ × 1𝑘 = 100 𝑚𝑉
2
Current range for 5 kΩ,
𝑉𝑠 100
𝐼= = = 20 𝑚𝐴
5𝑘 5𝑘
Current range for 20 kΩ,
𝑉𝑠 100
𝐼 = = = 5 𝑚𝐴 20𝑘 20𝑘
To measure 20 mA current, values of resistances are:
𝑉𝑠 = 𝐼𝑠(𝑅1 + 𝑅2 + 𝑅3)
Where, 𝐼𝑠 = 𝐼 − 𝐼𝑚 = 20𝑚 − 0.1𝑚 = 19.9 𝑚𝐴
𝑉𝑠 100𝑚
⇒ 𝑅1 + 𝑅2 + 𝑅3 = = = 5.02 Ω
𝐼𝑠 19.9𝑚
Where, 𝑅1 = 3 Ω, 𝑅2 = 1.02 Ω and 𝑅3 = 1 Ω.
To measure 5 mA current, values of resistances are:
𝐼𝑠 = 𝐼 − 𝐼𝑚 = 5𝑚 − 0.1𝑚 = 4.9 𝑚𝐴
𝑉𝑠 100𝑚
⇒ 𝑅1 + 𝑅2 + 𝑅3 = = = 20.4 Ω
𝐼𝑠 4.9𝑚
Where, 𝑅1 = 7.3 Ω, 𝑅2 = 7.1 Ω and 𝑅3 = 6 Ω.
Simulation:
The given circuit is simulated in Multisim.
A variable resistor of 40 kΩ is used and set to 12.5%, which gives a value of 5 kΩ. The values
of R1, R2, and R3 are used as calculated. Since Multisim does not explicitly include a PMMC
galvanometer component in its library, it is modeled using a DC voltage source connected in
series with a resistor (Rm). The simulation is shown in Figure 2.
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Figure 2: Multisim simulation for 5 kΩ resistance
For variable resistance 5 kΩ and calculated current 20mA, the circuit is simulated and the
values of Is and I are shown in Figure 3.
XMM1 displays current I, which is the total current flowing in the circuit and XMM2 displays
current Is which is flowing through the circuit consisting variable resistor.
Figure 3: Measured
current
Now, for 20 kΩ, variable resistance is set to 50% and calculated current is 5 mA, and
calculated values of resistors are used in simulation.
4
Figure 3: Measured current
Comparison:
The calculated and measured values of Is are exactly the same, but the values of I differ. The calculated
5 kΩ, while the simulated value is 19.98 mA, which is approximately 20 mA. Similarly, the calculated
v 20 kΩ, whereas the simulated value is 4.995 mA. The difference may be attributed to systematic
errors, approximations in calculations, limitations of the simulation software, or minor differences in the
model compared to ideal values.
