An ideal diode has been connected across a 10 Ω, 100 mA, centerzero PMMC meter as shown in figure.
The meter will read
In positive half cycle, the diode gets forward biased. Hence diode is in on state so, no current will flows through ammeter.
In negative half cycle, the diode gets reverse biased. Hence diode is in off state. So, the current flows through ammeter.
The current waveform will be,
PMMC instrument measures average value.
The deflecting torques of an ammeter varies as the square of the current passing through it. If a current of 15A produces a deflection of 30°, The deflection of a current of 20 A when instrument is spring controlled will be _____________ (in degrees).
T_{d} = K_{d}I^{2}
for spring control T_{c} = K_{c}θ
A moving iron instrument has 10 Ω resistance and gives full scale deflection when carrying 50 mA. It can be used measure 750 V by using what resistance?
Given that,
Full scale deflection = 50 mA
Internal resistance of instrument = 10 Ω
We can increase the range of voltage by using series resistance.
750 = (10 + R_{S}) × 50 × 10^{3}
⇒ R_{S} + 10 = 15,000
⇒ R_{S} = 14990 Ω
Hence the resistance should be connected in series.
What will be the reading (in V) when a voltage e = 200 sin ωt + 40 sin (3ωt + 30°) + 30 cos (5 ωt + 21.5°) v is applied to an electrodynamometer voltmeter.
Electrodynamometer voltmeter reads the rms value.
Given that,
e = 200 sin ωt + 40 sin (3ωt + 30°) + 30 cos (5 ωt + 21.5°) V
A 600 kΩ resistor is connected from the 200 V terminal to the common terminal of a dual scale voltmeter, as shown in figure (a). This modified voltmeter is then used to measure the voltage across the 360 kΩ resistor in the circuit in figure (b). What is the reading on the 500 V scale of the meter?
From the figure (a)
Internal resistance of galvanometer = 50 mV/1 mA
= 50 Ω
Now the circuit becomes,
Total internal resistance of voltmeter for 500 V scale,
R_{m} = 300 + [(199.5 + 0.05)600]
= 300 + [200600]
= 300 + 150 = 450 kΩ
Now, the voltmeter with internal resistance of 450 kΩ and 500 V scale is used to measure voltage in the circuit shown in fig (b).
Now, the circuit becomes
Because of voltmeter resistance, the load resistance becomes = 360450 = 200 kΩ
By voltage division,
The spring constant of a 3000 V electrostatic voltmeter is 7.06 × 10^{6} Nm/rad. The full scale deflection of the instrument is 80°. Assuming the rate of change of capacitance with angular deflection to be constant over the operating range. Calculate the total change of capacitance (in pF) from zero to full scale.
We know that,
Given that,
V = 3000 V
K = 7.06 × 10^{6} Nm/rad
Two different a.c, voltmeters are used to measure the voltage across the 22 kΩ resister shown in figure. Meter A has a.c. sensitivity of 10 kΩ/V, a guaranteed accuracy of 98% at full scale, and is set on its 200V scale. Meter B has an a.c. sensitivity of 4kΩ/V. a guaranteed accuracy of 98.5% at full scale, and is set on its (0100)V range. Which meter Provides more accurate results?
Sensitivity of meter A, S_{A} = 10 kΩ/V
Full scale reading of meter A, V_{FSD(A)} = 200 V
Internal resistance of meter A,
R_{V(A)} = 10 kΩ/V × 200 V
= 2000 KΩ
Guaranteed accuracy of Meter A = 98% at FSD.
Error of meter
Sensitivity of meter B, S_{B} = 4KΩ/V
Full Scale reading of meter B, V_{FSD} = 100V
Internal resistance of meter B,
R_{V(B)} = 4 KΩ/V × 100 = 400 KΩ
Guaranteed accuracy of meter B = 98.5% at FSD
Error of meter
True reading across 22 KΩ resister
If we use meter A, then the reading will be the effective will be, The effective resistance across 22kΩ
= 22k 2000k = 21.76 kΩ
Now the reading
But the meter has an error of 4V
Hence the range of reading = [49.71, 57.71]
If we use meter B, then the reading will be
The effective resistance across 22kΩ,
= 22k400k = 20.85kΩ
Now, the reading
But the meter has an error of 1.5V
Hence, the range of reading = [50.75, 53.75]
By observing both the readings we can conclude that meter B provides accurate results.
A moving iron instrument is calibrated with full scale deflection on 100 V DC. This instrument is used to measure 100 V at 50 Hz supply. Find the percentage error in reading if the instrument has a resistance of 2 kΩ and an inductance of 0.5 H
Full scale deflection of instrument (V_{FSD}) = 100V
Resistance (R_{m}) = 2 kΩ
Inductance (L_{m}) = 0.5 H
X_{L} = 2πfL = 2π × 50 × 0.5 = 157.08 Ω
Current through meter when 100 V at 50 Hz supply is applied
Voltage reading of meter
An input voltage represented by wave from as shown below is applied to a PMMC instrument. The reading of the instrument will be __ ( in V)
PMMC measures average value.
The average value
The coil of a moving coil voltmeter is 50 mm long and 40 mm wide and has 120 turns on it. The control spring exerts a torque 200 × 10^{6} n – m when the deflection is 100 divisions on full scale. If the flux density of the magnetic field in the air gap is 1.2 wb/m^{2}. The resistance that must be put in series with the coil to give one volt per division.
T_{c} = 200 × 10^{6} N – m
T_{d} = B I N A
= 1.2 × I × 120 × 50 × 40 × 10^{6}
= 288 × 10^{3} I n – m
At equilibrium,
T_{c} = T_{d}
⇒ 200 × 10^{6} = 288 × 10^{3} I
⇒ I = 0.694 mA.
Let the resistance of the voltmeter circuit be R voltage across the instrument = 0.694 × 10^{3} R
This produces a deflection of 100 divisions.
Volts per division
This value should be equal to 1 in order to get 1 volt per division.
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