Electric machinery fundamentals
5th Edition
ISBN: 9780073529547
Author: Chapman, Stephen J.
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Question
Chapter 1, Problem 1.21P
(a)
To determine
The initial force and initial current flow in the bar at starting.
(b)
To determine
The no-load steady state speed of the bar.
(c)
To determine
New steady-state speed of the bar after loading. Efficiency of the machine under these circumstances.
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A square loop of wire is oriented in a 12-tesla magnetic field directed to the left as shown.
The loop has a side length of 30 cm. At time t = 0, the loop is connected to a battery that results in 4 amps of current traveling counter-clockwise through the loop. Determine the magnitude and direction of the net torque acting on the loop the instant after the battery is connected. For the direction, imagine that you are looking at the loop from above.
In figure, a magnetic flux of F is generated with a constant current of i. The core material used has a relative permeability of 4000. Assuming that the mean cross sectional area that the magnetic flux passing through in core is A=4 [cm2] and there is no fringing in air gap, N= 1000 turns and i=10 [A], lair=2 [mm].
what is the reluctance in air gap?
what is the total reluctance?
what are the flux and flux density in air gap?
Remember: µ0 = 4πx10-7
In figure, a magnetic flux of F is generated with a constant current of i. The core material used has a relative permeability of 4000. Assuming that the mean cross sectional area that the magnetic flux passing through in core is A=4 [cm2] and there is no fringing in air gap, N= 1000 turns and i=10 [A], lair=2 [mm].
what is the reluctance in air gap?
what is the total reluctance?
what are the flux and flux density in air gap?
Remember: µ0 = 4πx10-7
Answers:Rair = ___________ [At/Wb]Rtotal = _________ [At/Wb]φ = ___________ [Wb]B = ________[T]
Chapter 1 Solutions
Electric machinery fundamentals
Ch. 1 - What is torque? What role does torque play in the...Ch. 1 - What is Amperes law?Ch. 1 - What is magnetizing intensity? What is magnetic...Ch. 1 - How does the magnetic circuit concept aid in the...Ch. 1 - What is reluctance?Ch. 1 - What is a ferromagnetic material? Why is the...Ch. 1 - How does the relative permeability of a...Ch. 1 - Prob. 1.8QCh. 1 - What are eddy current losses? What can be done to...Ch. 1 - Why are all cores exposed to ac flux variations...
Ch. 1 - What is Faraday law?Ch. 1 - What conditions are necessary for a magnetic field...Ch. 1 - What conditions are necessary for a magnetic field...Ch. 1 - Prob. 1.14QCh. 1 - The linear machine in Figure 1-19 is running at...Ch. 1 - Just how does a decrease in flux produce an...Ch. 1 - Will current be leading or lagging voltage in an...Ch. 1 - What are real, reactive, and apparent power? What...Ch. 1 - What is power factor?Ch. 1 - Prob. 1.1PCh. 1 - A flywheel with a moment of inertia of 4kgm2 is...Ch. 1 - A force of 10 N is applied to a cylinder of radius...Ch. 1 - A motor is supplying 50Nm of torque to its load....Ch. 1 - A ferromagnetic core is shown in Figure P1-2. The...Ch. 1 - A ferromagnetic core with a relative permeability...Ch. 1 - A two-legged core is shown in Figure P1-4. The...Ch. 1 - A core with three legs is shown in Figure P1-5....Ch. 1 - A two-legged core is shown in Figure P1-4. The...Ch. 1 - A wire is shown in Figure P1-7 that is moving in...Ch. 1 - Repeat Problem 1-10 for the wire in Figure P1-8.Ch. 1 - Prob. 1.12PCh. 1 - A core with three legs is shown in Figure P1-10....Ch. 1 - A two-legged magnetic core with an air gap is...Ch. 1 - A transformer core with an effective mean path...Ch. 1 - The core shown in Figure P1-2 has the flux shown...Ch. 1 - Prob. 1.17PCh. 1 - Prob. 1.18PCh. 1 - Prob. 1.19PCh. 1 - Demonstrate that Equation (1-59) can be derived...Ch. 1 - Prob. 1.21PCh. 1 - Prob. 1.22PCh. 1 - For the linear machine of Problem 1-22: When this...
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- Q2 A linear machine shown in Figure has a magnetic flux density of 0.5 T di rected into the page, a resistance of 0.25, a bar length / 1.0 m, and a battery voltage of 100 V. (a) What is the initial force on the bar at starting? What is the initial current flow? (b) What is the no-load steady-state speed of the bar? (c) If the bar is loaded with a force of 25 N opposite to the direction of motion, what is the new steady-state speed? What is the efficiency of the machine under these circumstances?arrow_forwardAt low slip, the relation between the torque and the slip is: Select one: a. τind is linearly proportional to S2 b. τind is linearly proportional to S c. τind is inversely proportional to S2 d. τind is inversely proportional to Sarrow_forwardA solenoid similar to the figure below, has a core made of cast steel (refer to the figure on the next slide). It has a cross-sectional area of 4cm2 and a mean length of 20cm. The coil has 100turns, and the coil current is 3.2A. Find the following: a)magnetomotive force, mmf b)magnetic field intensity, H c)flux density, Barrow_forward
- the torque-velocity (T/(w)) relations of the two machines with their shafts clamped together at constant voltage; T1(w)=a1-b1w a1=150Nm b1=1Nm . s/rad T2(w)=a2-b2w a2=270Nm b2=2Nm . s/rad friction will be neglected and there is also no load. In the clamped state, both will try to rotate in the same direction and if voltage is applied in the directions, find the torque, speed and operating mode (motor or generator) of each machine.arrow_forwardTo a magnetic core, with a relative permeability of 2100, a current I1 of 1 A and a current I2 of 2 A are applied, where the number of turns of the winding is 1000. The depth of the magnetic core is 20 cm. take into account that the bounded measurements are given in centimeters. The air gap shown in the figure is 0.2 cm and has an effective area equivalent to 1.1 times the cross-sectional area of the core. Determine:a) The equivalent circuit with sources and reluctance (Graph it)b) The magnetic flux of the central columnc) Magnetic induction at point Ad) Explain what would happen if the flow of current I1 is reversedarrow_forwardA solenoid similar to the figure below, has a core made of caststeel (refer to the figure on the next slide). It has a cross-sectional area of 4cm2 and a mean length of 20cm. The coil has 100turns, and the coil current is 3.2A. Find the following:a)magnetomotive force, mmfb)magnetic field intensity, Hc)flux density, B (with graph)arrow_forward
- A solenoid similar to the figure below, has a core made of cast steel (refer to the figure on the next slide). It has a cross-sectional area of 4cm2 and a mean length of 20cm. The coil has 100turns, and the coil current is 3.2A. Find the following: d)Permeability, μ e) the relative permeability, μr f) the core reluctance, R and g) the flux, Øarrow_forwardA rectangular loop carrying current I2 is placed parallel to an infinitely long filamentarywire carrying current I1 as shown in figure. Show that the force experienced by the loopis given byarrow_forwardA wire with negligible resistance is arranged in a magnetic field with a strength of 20 T oriented into the page as shown. A slider with a mass of 250 grams is connected to the fixed wire and can slide without friction. The slider has a resistance of 3 ohms. When the slider is released from rest, it begins to accelerate downward but quickly reaches a constant velocity. a) Determine the magnitude and direction of the current in the slider as it falls at a constant speed. b) Determine the induced emf in the loop as the slider falls at a constant speed. c) Determine the speed at which the slider falls. d) If the resistance of the slider is increased, will the constant speed of the slider be lower, higher, or the same as determined in part c? Justify your answer.arrow_forward
- . A mild steel ring of 30 cm mean circumference has a cross-sectional area of 6 cm2and has a winding of 500 turns on it. The ring is cut through at a point so as to provide an air-gap of 1 mm in the magnetic circuit. It is found that a current of 4 A in the winding, produces a flux density of 1 T in the air-gap. Find the relative permeability of the mild steelarrow_forwardA permanent magnet is held in a vertical position on top of a loop of wire that is in the horizontal plane, as shown in the figure. The south pole of the magnet points towards the loop. After leavingIf the magnet falls, which of the following statements is true regarding the induced current in the loop, if viewed from above?i). The current rotates in a clockwise direction as the magnet approaches the loop.ii). The current rotates counterclockwise as the magnet approaches the loop.iii). The current rotates in a clockwise direction when the magnet has already passed through the loop and is moving away from it.iv). the current always goes in a clockwise direction.v). The current goes counterclockwise as the magnet approaches the loop, and then goes clockwise as it passes the loop.Clearly explain your answers.arrow_forwardSOLVE AND SHOW YPUR COMPLETE SOLUTION. ANSWERS SHOULD BE IN TWO DE CIMAL PLACES. The armature of a two-pole dc machine has 30 slots, each slot has 4 conductors each. during its operation, only 75% of the conductors are directly under the pole. each pole measures 2 inches by 3 inches and produces ten million maxwells of flux. the armature core is 12 inches in length and 3.5 inches in diameter. the total resistance of the winding is 2 ohms. a) determine the frequency of the machine when running at 3600 rpm.arrow_forward
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