Please wait...
/
-
In a 3 ½ digit digital multimeter, there are three full digits and one half digit.
A full digit counts from 0 to 9 whereas an half digit counts from 0 to 1.
Concept:
The resolution in a N bit DVM is given by =110N×rangeofvoltage
Where N is the number of full digits.
In a DVM, a full digit counts 0 to 9 and half digit counts from 0 to 1.
Calculation:
The full-scale reading = 9.99 V
It is a 3-digit voltmeter.
Range of voltmeter = 10 V
Resolution for the given DVM is =1103×10=0.01
Resistance (R) = 100 kΩ
Capacitance (C) = 1 μF
Integrator input voltage (Vi) = 1 V
For an integrator type DVM, output voltage is given by
V0=−1RC∫0tVidt
=−1100×103×1×10−6∫011dt=−10V
We know that,
Average value of triangular wave = Vm2
rms value of triangular wave =Vm3
⇒Vm30=60⇒Vm=603
Analog instrument:
Voltage error = ±2% of 25 V = ±0.5 V
Error =±0.520×100=±2.5%
Digital instrument:
For 20 V displayed on 3 ½ digit display, 1 digit = 0.01 V
Voltage error = ±(0.6% of reading + 1 count)
= ±(0.12 + 0.01) = ±0.13 V
For a dual-slope analog to digital converter,
De-integration time, T2=ViVRef×T1
Where Vi = input voltage
VRef = reference voltage
T1 is the first integration time
Total conversion time = first integration time (T2) + de-integration time.
Given that, input voltage (Vi) = 6.8 mV
Reference voltage (VR) = 10 mV
Integration time (T1) = 10 ms
De-integration time, T2=6.810×10=6.8ms
T1 = nTs
⇒150clks=n×1fs
⇒150×Tclk=n×1fs
⇒150×1fclk=n×1fs
⇒fclk=fs×150n
For maximum clock frequency, the value of n should be i.
Let the voltage is VS and the internal resistance is R
For 5 V scale:
Internal resistance = full scale voltage × sensitivity
= 5 V × 20 kΩ/V = 100 kΩ
Reading = 4.5 V
⇒VS×(100R+100)=4.5
For 10 V scale:
= 10 V × 20 kΩ/V = 200 kΩ
Reading = 6 V
⇒VS×(200R+200)=6
By solving the above two equations, we get
The dc sensitivity =1100×10−6=10kΩ/v
For a halfwave rectifier,
Ac sensitivity = 0.45 × dc sensitivity
= 0.45 × 10 = 4.5 kΩ/v
Series multiplier = (Sac) (V) - Rm - Rd
= (4.5)(20) – 2 – 0.5
The meter uses a full wave rectifier circuit it indicates value of 2.77 V the form factor for full wave rectified sinusoidal waveform is 1.11
Average value of voltage, Vavg = 2.49 V
For triangular wave shape, peak value of voltage Vm = 2 Vavg = 4.98 V
Vrms=Vm3=4.983=2.87V%error=2.77−2.872.87×100=−3.48%
Correct (-)
Wrong (-)
Skipped (-)