Large AC ammeters use a high-permeability core that can be clamped around the current to be measured, as shown in the top right. Lets use a simple toroidal model for the clamp as shown below, where the toroid has a mean radius , and cross-sectional area A. A secondary winding of N turns is wrapped on this toroidal core. a. Assuming the current passes through the center of the torus, find the B field inside the core at the mean radius r. b. If the AC current to be measured is expressed as I(t)=1 cos(@t), find an expression for the induced secondary voltage V(t). Use the result of (a) and assume that the magnetic field is approximately constant over the cross section of the core. c. How many turns in the secondary winding would be required to insure that the induced AC voltage amplitude is at least 10 mV for 60 Hz currents of >1 A? Assume core dimensions H4, = 5000. V(t) Ntu of r = 2 cm and A=0.25 cm

Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter6: Power Flows
Section: Chapter Questions
Problem 6.45P
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Large AC ammeters use a high-permeability core
that can be clamped around the current to be
measured, as shown in the top right. Lets use a
simple toroidal model for the clamp as shown
below, where the toroid has a mean radius , and
cross-sectional area A. A secondary winding of
N turns is wrapped on this toroidal core.
a. Assuming the current passes through the
center of the torus, find the B field inside the
core at the mean radius r.
b. If the AC current to be measured is
expressed as I(t)=1,cos(@t), find an
expression for the induced secondary
voltage V(t). Use the result of (a)
and assume that the magnetic field
is approximately constant over the
cross section of the core.
V(t)
1251
N turns
ww
c. How many turns in the secondary
winding would be required to insure
that the induced AC voltage
amplitude is at least 10 mV for 60
Hz currents of >1 A? Assume core
dimensions of r = 2 cm and A=0.25 cm², and a relative permeability of
H4, = 5000.
1(t)
Transcribed Image Text:Large AC ammeters use a high-permeability core that can be clamped around the current to be measured, as shown in the top right. Lets use a simple toroidal model for the clamp as shown below, where the toroid has a mean radius , and cross-sectional area A. A secondary winding of N turns is wrapped on this toroidal core. a. Assuming the current passes through the center of the torus, find the B field inside the core at the mean radius r. b. If the AC current to be measured is expressed as I(t)=1,cos(@t), find an expression for the induced secondary voltage V(t). Use the result of (a) and assume that the magnetic field is approximately constant over the cross section of the core. V(t) 1251 N turns ww c. How many turns in the secondary winding would be required to insure that the induced AC voltage amplitude is at least 10 mV for 60 Hz currents of >1 A? Assume core dimensions of r = 2 cm and A=0.25 cm², and a relative permeability of H4, = 5000. 1(t)
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