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1624 The high-voltage side of a transformer has 750
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turns, and the low-voltage side 50 turns When the high side is connected to a rated voltage of 120 V, 60 Hz, a rated load of 40 A is connected to the low side Calculate a The turns ratio b The secondary voltage (assuming no internal transformer impedance voltage drops) c The resistance of the load
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1625 A transformer is to be used to match an 8loudspeaker to a 500- audio line What is the turns ratio of the transformer, and what are the voltages at the primary and secondary terminals when 10 W of audio power is delivered to the speaker Assume that the speaker is a resistive load and the transformer is ideal 1626 The high-voltage side of a step-down transformer has 800 turns, and the low-voltage side has 100 turns A voltage of 240 VAC is applied to the high side, and the load impedance is 3 (low side) Find a The secondary voltage and current b The primary current c The primary input impedance from the ratio of primary voltage and current d The primary input impedance
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1632 Derive the same result obtained in
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Example 1611 using equation 1646 and the de nition of inductance given in equation 1630 You will rst compute the inductance of the magnetic circuit as a function of the reluctance, then compute the stored magnetic energy, and nally write the expression for the magnetic force given in equation 1646
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1633 With reference to Example 1611, generate a
simulation program (eg, using SimulinkTM ) that accounts for the fact that the solenoid inductance is not constant, but is a function of plunger position Compare graphically the current and force step responses of the constant-L simpli ed solenoid model to the step responses obtained in Example 1611
1627 Calculate the transformer ratio of the transformer
in Problem 1626 when it is used as a step-up transformer 1628 A 2,300/240-V, 60-Hz, 46-kVA transformer is designed to have an induced emf of 25 V/turn Assuming an ideal transformer, nd a The number of high-side turns, Nh , and low-side turns, Nl b The rated current of the high-voltage side, Ih c The transformer ratio when the device is used as a step-up transformer
1634 With reference to Example 1612, calculate the
required holding current to keep the relay closed
1635 The relay circuit shown in Figure P1635 has the
following parameters: Agap = 0001 m2 ; N = 500 turns; L = 002 m; = 0 = 4 10 7 (neglect the iron reluctance); k = 1000 N/m, R = 18 What is the minimum DC supply voltage, v, for which the relay will make contact when the electrical switch is closed
Movable part Switch R Spring k N M
Section 4: Electromechanical Transducers 1629 For the electromagnet of Example 169:
a Calculate the current required to keep the bar in place (Hint: The air gap becomes zero and the iron reluctance cannot be neglected) b If the bar is initially 01 m away from the electromagnet, what initial current would be required to lift the magnet
1630 With reference to Example 1610, determine the
best combination of current magnitude and wire diameter to reduce the volume of the solenoid coil to a minimum Will this minimum volume result in the lowest possible resistance How does the power dissipation of the coil change with the wire gauge and current value To solve this problem you will need to nd a table of wire gauge diameter, resistance, and current ratings Table 22 in this book contains some information The solution can only be found numerically 1631 Derive the same result obtained in Example 1610 using equation 1646 and the de nition of inductance given in equation 1630 You will rst compute the inductance of the magnetic circuit as a function of the reluctance, then compute the stored magnetic energy, and nally write the expression for the magnetic force given in equation 1646
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Figure P1635
1636 The magnetic circuit shown in Figure P1636 is a
very simpli ed representation of devices used as surface roughness sensors The stylus is in contact with the surface and causes the plunger to move along with the surface Assume that the ux in the gap is given by the expression = /R(x), where is a known constant and R(x) is the reluctance of the gap The emf e is measured to determine the surface pro le Derive an expression for the displacement x as a function of the various parameters of the magnetic circuit and of the measured emf (Assume a frictionless contact between the moving plunger and the magnetic structure and that the plunger is restrained to vertical motion only The cross-sectional area of the plunger is A)
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