16. A single-phase, 1/4 hp, 230 V, 60 Hz, four-pole, 1710 rpm induction motor has the followingequivalent circuit parameters for the main winding: Rim=9.52, R02=10.82, X1m=X'2=122, Xmag=2602At 230V and rated speed, the core loss is 30W, and the friction and windage loss is 15W. The motor isconnected to an 1 ø, 230V, 60HZ supply and runs at the rated speed. Determine:a) The slip.b) The motor current.c) The input power factor.d) The input power.e) The developed torque.f) The output shaft power and shaft torque.g) The efficiency.h) The rotor circuit frequencies and the rotor cu-losses.i) The ratio of the forward flux to the backward flux.

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16. A single-phase, 1/4 hp, 230 V, 60 Hz, four-pole, 1710 rpm induction motor has the following equivalent circuit parameters for the main winding: Rịm=9.52, R02=10.82, X1m=X2=122, Xmag=2602 At 230V and rated speed, the core loss is 30W, and the friction and windage loss is 15W. The motor is connected to an 1 q, 230V, 60HZ supply and runs at the rated speed. Determine: a) The slip. b) The motor current. c) The input power factor.

16. A single-phase, 1/4 hp, 230 V, 60 Hz, four-pole, 1710 rpm induction motor has the following equivalent circuit parameters for the main winding: Rịm=9.52, R02=10.82, X1m=X2=122, Xmag=2602 At 230V and rated speed, the core loss is 30W, and the friction and windage loss is 15W. The motor is connected to an 1 q, 230V, 60HZ supply and runs at the rated speed. Determine: a) The slip. b) The motor current. c) The input power factor.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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3. The slip-ring rotor resistance and standstill reactance per phase of a 3300 V, 24-pole, 50 Hz, 3-phase star-connected induction motor are 0.02 ohm and 0.3 ohm respectively. Calculate the (a) speed at maximum torque (b) ratio of full load torque to maximum torque if the full load speed is 246 rpm
16. A single-phase, 1/4 hp, 230 V, 60 Hz, four-pole, 1710 rpm induction motor has the following equivalent circuit parameters for the main winding: R1m=9.5Ω, R02=10.8Ω, X1m=X/2=12Ω, Xmag=260Ω At 230V and rated speed, the core loss is 30W, and the friction and windage loss is 15W. The motor is connected to an 1 φ, 230V, 60Hz supply and runs at the rated speed. Determine:a) The slip.b) The motor current.c) The input power factor.d) The input power.e) The developed torque.f) The output shaft power and shaft torque.g) The efficiency.h) The rotor circuit frequencies and the rotor cu-losses.i) The ratio of the forward flux to the backward flux.
A single-phase, 120 V, 60 Hz, four-pole, split-phase induction motor has the following equivalentcircuit parameters: R1m=1.5Ω, R1a=2.5Ω, R/2=1Ω, X1m=2.5Ω, X1a =2.5Ω, X/2=1.5Ω, Xmag =40Ωa) Determine the standstill impedances (Zm, Za) of the windings.b) Determine the starting torque and the starting current of the motor if it is started from rated voltagemains as a resistor split-phase motor.c) Determine the value of the capacitor to be connected in series with the auxiliary winding toproduce maximum starting torque per ampere of starting current. Determine the value of thestarting torque and starting current.d) Compare the starting torque per ampere of starting current for cases (b) and (c)
18. A single-phase, 120 V, 60 Hz, four-pole, split-phase induction motor has the following standstill impedances:Main winding: Zm =5+j6.25Auxiliary winding: Za =8+j6a) Determine the value of capacitance to be added in series with the auxiliary winding to obtain maximum starting torque.b) Compare the starting torques and starting current with and without the added capacitance in the auxiliary winding circuit when operated from a 120V, 60Hz supply.
6. A 15 HP, 4 pole, 220 volts three phase star connected, 1725 rpm induction motor has the following parameters: R1 = 0.15 Ω, R2 = 0.18 Ω, X1 = 0.31 Ω and X2 = 0.31 Ω, friction and windage loss = 240 watts. Determine (i) Slip at maximum torque and maximum torque in synchronous torque (ii) slip at maximum power and maximum power (iii) starting torque and starting current.
The equivalent circuit parameters of a 230-V, 1-phase, 6-pole, 60-Hz induction motor are: R1 = R2’ =10ohm, X1 = X2’ = 10ohm, and Xm = 100ohm. At a slip of 5%, calculate the developed torque and The input power to the motor at 230V, while running on no-load, is 31.4 W at 1.2 A. What is the approximate efficiency of the motor at 5% slip?
A 4-pole, 115 V, 60 Hz, 1710 rpm, capacitor-start single-phase induction motor has been designed to produce maximum starting torque per unit starting current. The motor has the following parameters: R1m=1.5ohms, X1m=2.6ohms, R1a=2.5 ohms, X1a=2.5 ohms, Xmag=40 ohms, R/2=1 ohms, X/2=1.6 ohmsNa/Nm =l, Capacitor in series with auxiliary winding = 375 μF.a) Draw the equivalent circuit for the motor under starting conditions. Determine the value of the starting torque.b) Draw the equivalent circuit for the motor when it runs at the rated (i.e., full load) speed. Determine the torque developed at this speed.c) Determine the ratio of the starting torque to the torque developed at the rated speed.
A three phase, 4 pole, 3300 V, 50 Hz, star connected Induction motor, has identical primary and referred secondary impedance of value 3+j9 Ohm per phase. Using the approximate circuit, calculate: A. The full load torque at rated slip of 5%. B. The maximum torque at normal voltage and frequency.
A 3300-V, 50-Hz, 3-phase, 4-pole, star-connected induction motor has identical primary and referred secondary impedances of value 3 + j9 ohm per phase. The turns-ratio per phase is 3/I (stator/rotor), and the rotor winding is connected in delta and brought out to slip rings. Calculate: the full-load torque at rated slip of 5%; the maximum torque at normal voltage and frequency; the supply voltage reduction which can be withstood without the motor stalling; the maximum torque if the supply voltage and frequency both fall to half normal value; the increase in rotor-circuit resistance which, at normal voltage and frequency, will permit maximum torque to be developed at starting. Express this: as a fraction of normal R2and as (3) ohmic values to be placed in series with each of the slip-ring terminals and star connected.
A 4-pole, 3-phase, 50Hz induction motor has a voltage between slip-rings on open circuit of 520V. The star connected rotor has a standstill reactance and resistance of 2.0 and 0.4 Ω per phase respectively. Determine: (a) The full-load torque if full load speed is 1,425 rpm(b) The ratio of starting torque to full-load torque(c) The additional rotor resistance required to give maximum torque at standstill.
A four-pole, single-phase, 120 V, 60 Hz induction motor gave the following standstill impedances when tested at rated frequency:Main winding : Zm =1.5+j4 ohmsAuxiliary winding : Za =3+j6 ohmsa) Determine the value of external resistance to be inserted in series with the auxiliary winding to obtain maximum starting torque as a resistor split-phase motor.b) Determine the value of the capacitor to be inserted in series with the auxiliary winding to obtain maximum starting torque as a capacitor-start motor.c) Determine the value of the capacitor to be inserted in series with the auxiliary winding to obtain maximum starting torque per ampere of the starting current as a capacitor-start motor.d) Compare the starting torques and starting currents in parts (a), (b), and (c) expressed as per unit of the starting torque without any external element in the auxiliary circuit, when operated at 120V, 60Hz.
A 3-phase induction motor, 440-V, 50-Hz, 6-pole, delta-connected has the following equivalent-circuit parameters at normal frequency:R1.2 ohm, R'2=0.18 ohm, X1= x'2=0.58 ohm, all per phase values. The machine is subjected in service to an occasional fall of 40% in both voltage and frequency. What total mechanical load torque is it safe to drive so that the machine just does not stall under these conditions? When operating at normal voltage and frequency, calculate the speed when delivering this torque and the power developed. Calculate also the speed at which maximum torque occurs. If V and f were both halved, what would be the increase in starting torque from the normal direct-on-line start at rated voltage and frequency? If now the machine is run up to speed from a variable-voltage, variable-frequency supply, calculate the required terminal voltage and frequency to give the 'safe' torque calculated above: (i) at starting, (ii) at 500 rev/min. Repeat (d) for the machine to develop a…