1.17 Potential
divider arrangement
The resistance R1, R2 , R3 and R4 is connected in series to
obtained the ranges V1,V2 ,V3 and V4
Example: 1.1
A PMMC ammeter has the following specification
Coil dimension are 1cm × 1cm. Spring constant is 0.15 × 10−6 N − m / rad , Flux density is 1.5 × 10−3 wb / m2 .Determine the no. of turns required to produce a deflection of 900 when a current 2mA flows through the coil.
Solution:
At steady state condition
Td = TC
The pointer of a moving coil instrument gives full scale deflection of 20mA. The potential difference across the meter when carrying 20mA is 400mV.The instrument to be used is 200A for full scale deflection. Find the shunt resistance required to achieve this, if the instrument to be used as a voltmeter for full scale reading with 1000V. Find the series resistance to be connected it?
Solution:
Case-1
Vm =400mV
Im = 20mA
I=200A
Example: 1.2
The coil of a 600V M.I meter has an inductance of 1 henery. It gives correct reading at 50HZ and requires 100mA. For its full scale deflection, what is % error in the meter when connected to 200V D.C. by comparing with 200V A.C?
Solution:
Example: 1.3
The relationship between inductance of moving iron ammeter, the current and the position of pointer is as follows:
Calculate the deflecting torque and the spring constant when the current is 1.5A?
Solution:
For current I=1.5A, θ =55.5 degree=0.96865 rad
Example: 1.4
For a certain dynamometer ammeter the mutual inductance ‘M’ varies with deflection θ as M = −6 cos(θ + 30° )mH .Find the deflecting torque produced by a direct current of 50mA corresponding to a deflection of 600 .
Solution:
Example: 1.5
The inductance of a moving iron ammeter with a full scale deflection of 900 at 1.5A, is given by the expression L = 200 + 40θ − 4θ2 − θ3 µH , where θ is deflection in radian from the zero position. Estimate the angular deflection of the pointer for a current of 1.0A.
Solution:
Example: 1.6
The inductance of a moving iron instrument is given by L = 10 + 5θ − θ2 − θ3 µH , where θ is the deflection in radian from zero position. The spring constant is 12 ×10−6 N − m / rad . Estimate the deflection for a current of 5A.
Solution:
Example: 1.7
The following figure gives the relation between deflection and inductance of a moving iron instrument.
Find the current and the torque to give a deflection of (a)
300 (b) 800 . Given that control spring constant is 0.4
×10−6 N − m / degree
Solution:
Example: 1.8
Solution:
Example: 1.9
Design a multi range d.c. mille ammeter using a basic
movement with an internal resistance Rm = 50Ω and a full scale deflection current Im = 1mA . The ranges required are 0-10mA;
0-50mA; 0- 100mA and 0-500mA.
Solution:
Case-I 0-10mA
Example: 1.10
A moving coil voltmeter with a resistance of 20Ω gives a
full scale deflection of 1200 , when a potential difference of 100mV
is applied across it. The moving coil has dimension of 30mm*25mm and is wounded
with 100 turns. The control spring constant is 0.375 ×10−6 N − m /
degree. Find the flux density, in the air gap. Find also the diameter of copper
wire of coil winding if 30% of instrument resistance is due to coil winding.
The specific resistance for copper=1.7 ×10−8 Ωm .
Solution:
Data given
Vm = 100mV
Rm = 20Ω
θ = 120°
N=100
Example: 1.11
A moving coil instrument gives a full scale deflection of 10mA, when the potential difference across its terminal is 100mV. Calculate
(1) The shunt resistance for a full scale deflection corresponding to 100A
(2) The resistance for full scale reading with 1000V.
Calculate the power dissipation in each case?
Solution:
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