# Example 10.1
# Computation of (a) Induced emf (b) Frequency of the rectangular voltage
# wave in the armature winding
# Page No. 394
# Given data
E1=136.8; # Generated emf
P=6.; # Number of poles
n=1180.; # Operating speed of machine
# (a) Induced emf
E2=E1*0.75*2.;
# (b) Frequency of the rectangular voltage wave in the armature winding
f=P*n*0.75/120.;
# Display result on command window
print"Induced emf =",E2,"V"
print"Frequency of the rectangular voltage wave =",f,"Hz"
# Example 10.2
# Computation of rheostat setting required to obtain an induced emf of 290 V
# Page No. 399
# Given data
Ebat=240.; # Induced emf
If=8.9; # Field current
Rf=10.4; # Field resistance
# Rheostat setting required to obtain an induced emf of 290 V
Rrheo=(Ebat/If)-Rf;
# Display result on command window
print"Rheostat setting to obtain an induced emf of 290 V =",Rrheo
# Example 10.3
# Computation of no-load voltage if the voltage regulation is 2.3 percent
# Page No. 401
# Given data
Vrated=240.; # Rated voltage
VR=0.023; # Voltage regulation
# No-load voltage if the voltage regulation is 2.3 percent
Vnl=Vrated*(1.+VR);
# Display result on command window
print"No-load voltage if the voltage regulation is 2.3 percent =",Vnl,"V"
# Example 10.4
# Computation of percentage reduction in field flux required to obtain a
# speed of 1650 r/min while drawing an armature current of 50.4 A.
# Page No. 405
# Given data
VT=240.; # Induced emf
R=95.2; # Shunt field resistance
IT=72.; # Total current
Ra=0.242; # Armature resistance
Ia2=50.4; # Armature current
n1=850.; # Rated speed of shunt motor
n2=1650.; # Speed of armature winding
# Percentage reduction in field flux
If1=VT/R; # Field current
Ia1=IT-If1; # Armature current
Ea1=VT-Ia1*Ra; # Armature emf
Ea2=VT-Ia2*Ra;
phip2=(n1/n2)*(Ea2/Ea1);
PerRed=(phip2-1.)*100.;
# Display result on command window
print"Percentage reduction in field flux =",PerRed,"Percent"
# Example 10.5
# Computation of no-load speed
# Page No. 408
# Given data
nrated=1750.; # Rated speed
SR=4.; # Speed regulation
# No-load speed
Snl=nrated*(1+SR/100);
# Display result on command window
print"No-load speed =",Snl,"r/min"
# Example 10.6
# Computation of Induced emf
# Page No. 418
# Given data
P=25000.; # Power of the generator
VT=250.; # Rated voltade of the machine
Ra=0.1053; # Armature resistance
Rip=0.0306; # Resistance of interpolar winding
Rcw=0.0141; # Resistance of compensating windings
# Induced emf
Ia=P/VT; # Armature current
Racir=Ra+Rip+Rcw; # Resistance of armature circuit
Ea=VT+Ia*Racir; # Induced emf
# Display result on command window
print"Induced emf =",Ea,"V"
# Example 10.7
# Computation of cemf
# Page No. 418
# Given data
Rf=408.5; # Field resistance
VT=500.; # Rated voltade of the machine
IT=51.0; # Total current
Ra=0.602; # Armature resistance
Ripcw=0.201; # Resistance of interpolar winding and compensating windings
# Induced emf
If=VT/Rf; # Current
Ia=IT-If; # Armature current
Racir=Ra+Ripcw; # Resistance of armature circuit
Ea=VT-Ia*Racir;
# Display result on command window
print"Induced emf =",Ea,"V"
# Example 10.8
# Computation of new armature current
# Page No. 420
# Given data
Rf=120.; # Resistance of inserted resistor
VT=240.; # Rated voltade of the machine
IT=91.; # Total current
Racir=0.221; # Armature sircuit resistance
n2=634.; # New speed after resistor was inserted
n1=850.; # Rated speed OF THE MACHINE
Rx=2.14; # Resistance inserted in series witH armature
# New armature current
If=VT/Rf; # Resistor current
Ia1=IT-If; # Armature current
Ia2=(VT-(n2/n1)*(VT-Ia1*Racir))/(Racir+Rx);
# Display result on command window
print"New armature current =",Ia2,"A"
# Example 10.9
# Computation of (a) Steady state armature current if a rheostat in the
# shunt field circuit reduces flux in air gap to 75% of its rated value
# (b) Steady state speed for the conditions in (a)
# Page No. 421
# Given data
Rf=160.; # Field resistance
VT=240.; # Rated voltade of the machine
IT=37.5; # Total current
Ra=0.213; # Armature resistance
Rip=0.092; # Resistance of interpolar winding
Rcw=0.065; # Resistance of compensating windings
n1=2500.; # Rated speed of the machine
# (a) At rated conditions
If=VT/Rf; # Field current
Ia1=IT-If; # Armature current
Ia2=Ia1*0.50*1./0.75;
# (b) steady state speed for the above mentioned conditions
Racir=Ra+Rip+Rcw;
n2=n1*(VT-(Ia2*(1.+Racir)))/0.75*(1./(VT-(Ia1*Racir)));
# Display result on command window
print"Steady state armature current =",Ia2,"A"
print"Steady state speed =",n2,"r/min"
# Example 10.10
# Computation of (a) Mechanical power developed (b) Torque developed
# (c) Shaft torque
# Page No.427
# Given data
T=40.; # Hp rating of motor
Rf=95.3; # Field resistance
VT=240.; # Rated voltade of the machine
IT=140.; # Total current
Racir=0.0873; # Armature circuit resistance
n=2500.; # Rated speed of the machine
# (a) The mechanical power developed
If=VT/Rf; # Field winding current
Ia1=IT-If; # Armature current
Ea=VT-Ia1*Racir; # Armature emf
Pmech=Ea*Ia1; # Mechanical power
Pmechhp=Ea*Ia1/746.;
# (b) Torque developed
TD=7.04*Ea*Ia1/n;
# (c) Shaft torque
Tshaft=T*5252./n;
# Display result on command window
print"Mechanical power developed=",Pmech,"%0.0f W ",Pmech
print"Mechanical power developed=",Pmechhp,"hp ",Pmechhp
print"Torque developed =",TD,"lb-ft "
print"Shaft torque =",Tshaft,"lb-ft "
# Example 10.11
# Determine (a) Electrical losses (b) Rotational losses (c) Efficiency
# Page No. 430
# Given data
T=124.; # Hp rating of motor
Rf=32.0; # Field resistance
VT=240.; # Rated voltade of the machine
IT=420.; # Total current
Ra=0.00872; # Armature resistance
RipRcw=0.0038; # Resistance of interpolar winding and compensating windings
Pout=92504.;
Vb=2.0; # Rated speed of the machine
Racir=Ra+RipRcw;
# (a) Electrical losses
If=VT/Rf; # Field current
Ia=IT-If; # Armature current
Pf=If**2.*Rf; # Field power
Paipcw=Ia**2.*(Ra+RipRcw);
Pb=Vb*Ia; # Brush loss power
Plosses=Pf+Paipcw+Pb; # Total power loss
# (b) Rotational losses
Ea=VT-(Ia*Racir)-Vb; # Armature emf
Pmech=Ea*Ia; # Mechanical power
Pshaft=T*746.; # Shaft power
Protational=Pmech-Pshaft;
# (c) Ffficiency
eeta=Pout/(VT*IT)*100.;
# Display result on command window
print"Electrical losses =",Plosses,"W"
print"Rotational losses =",Protational,"W"
print"Efficiency =",eeta,"Percent"
# Example 10.12
# Determine (a) Rated torque (b) Armature current at locked rotor if no
# starting resistance is used (c) External resistance required in the armature
# circuit that would limit the current and develop 200 percent rated torque
# when starting (d) Assuming the system voltage drops to 215V, determine the
# locked rotor torque using the external resistor in (c)
# Page No. 433
# Given data
n=1750.; # Rotor speed
P=15.; # Hp rating of motor
VT=230.; # Rated voltade of the machine
Ea=0;
Racir=0.280; # Armature circuit loss
Rf=137.; # Field resistance
ItRated=56.2; # Total current drawn
VT1=215.; # Rated voltage after drop
# (a) Rated torque
Trated=P*5252./n;
# (b) Armature current
Ia=(VT-Ea)/Racir;
# (c) External resistance required
If=VT/Rf; # Field current
IaRated=ItRated-If; # Rated armature current
Ia2=IaRated*2.; # Armature current for 200% rated torque
Rx=((VT-Ea)/Ia2)-Racir; # External resistance required
# (d) Locked rotor torque
If215=VT1/Rf; # Field current at 215V
Ia215=(VT1-Ea)/(Racir+Rx); # Armature current at 215V
TD2=Trated*( (If215*Ia215) / (If*IaRated) );
# Display result on command window
print"Rated torque =",Trated,"lb-ft "
print"Armature current =",Ia,"A"
print"Armature current for 200 percent rated torque =",Ia2," %0.1f A "
print"External resistance required =",Rx," %0.2f Ohm "
print"Locked rotor torque =",TD2,"lb-ft "