# Chapter 13 Alternating current circuits¶

## Example 13.1 page no 217¶

In [1]:
#given
Vm=100                           #Maximum voltage in V
R=50                             #resitance in ohms

#Calculations
import math
Vrms=(Vm/math.sqrt(2))
Irms=(Vrms/R)
Im=(Vm/R)

#Output
print"rms current is ",round(Irms,2),"A and maximum current is ",Im,"A"

rms current is  1.41 A and maximum current is  2 A


## Example 13.2 page no 218¶

In [2]:
#given
c=50                                  #Capacitor in micro F
Vm=220                                #Maximum voltage in V
f=50                                  #Frequency in Hz

#Calculations
import math
Xc=(1/(2.0*3.14*c*10**-6*f))
I=(Vm/Xc)
Irms=I/math.sqrt(2)

#Output
print"rms current is ",round(Irms,2),"A"

rms current is  2.44 A


## Example 13.3 page no 218¶

In [3]:
#given
L=2                                       #Inductance in H
Vrms=220                                  #rms voltage in V
f=50                                      #Frequency in Hz

#Calculations
Xl=(2*3.14*f*L)
Irms=(Vrms/Xl)

#Output
print"rms current is ",round(Irms,3),"A"

rms current is  0.35 A


## Example 13.4 page no 218¶

In [4]:
#given
Vm=220                          #Maximum voltage in V
f=50                            #frequency in Hz
R=2000                          #Resistance in ohms
C=5*10**-6                      #Capacitor in F

#Calculations
import math
Xc=(1/(2*3.14*f*C))
Z=math.sqrt(R**2+Xc**2)
Vc=(Vm*Xc)/Z

#Output
print"Maximum potential difference across the capacitor is ",round(Vc,1),"V"

Maximum potential difference across the capacitor is  66.8 V


## Example 13.5 page no 218¶

In [1]:
#given
R=5000                                   #Resistance in ohms
L=2                                      #Inductance in H
Vrms=200                                 #rms Voltage in V
f=50                                     #Frequency in Hz

#Calculations
import math
Xl=(2*3.14*f*L)
Z=math.sqrt(R**2+Xl**2)
Vl=(Vrms*Xl)/Z

#Output
print"rms potential difference across the inductor is ",round(Vl,2),"V"

rms potential difference across the inductor is  24.92 V


## Example 13.6 page no 218¶

In [5]:
#given
R=10.0                                        #Resistance in ohms
L=5*10**-3                                  #Inductance in H
C=10.0*10**-6                                 #Capacitance in F
V=100                                       #Voltage in V
f=50.0                                       #Frequency in Hz

#Calculations
import math
Xc=1/(2.0*3.14*f*C)
Xl=(2*3.14*f*L)
Z=math.sqrt(R**2+(Xl-Xc)**2)
I=(V/Z)
q=math.atan((Xl-Xc)/R)*180/3.14
Vr=(I*R)
Vc=(I*Xc)
Vl=(I*Xl)

#Output
print"Total impedence is ",round(Z,1),"ohms"
print"Current is ",round(I,2),"A"
print"Phase angle is ",round(q,1),"degrees"
print"Voltage across resistor is ",round(Vr,2),"V"
print"Voltage across capacitor is ",round(Vc,0),"V"
print"Voltage across inductor is ",round(Vl,3),"V"

Total impedence is  317.1 ohms
Current is  0.32 A
Phase angle is  -88.2 degrees
Voltage across resistor is  3.15 V
Voltage across capacitor is  100.0 V
Voltage across inductor is  0.495 V


## Example 13.7 page no 219¶

In [6]:
#given
R=5.0                                       #Resistance in ohms
L=2.0*10**-3                                #Inductance in H
C=25.0*10**-6                               #Capacitance in F
V=50                                      #Voltage in V

#Calculations
import math
w=1/math.sqrt(L*C)
f=(w/(2.0*3.14))
Q=(w*L)/R

#Output
print"Resonating frequency is ",round(f,0),"Hz"
print"Q factor is ",round(Q,2)

Resonating frequency is  712.0 Hz
Q factor is  1.79


## Example 13.8 page no 219¶

In [26]:
#given
L=(20*10**-3)                                    #Inductance in H
Q=8.0                                            #Q factor
f=1000                                           #Frequency in Hz

#Calculations
R=(2*3.14*f*L)/Q
C=(1/((2.0*3.14*f)**2*L))/10**-6

#Output
print"Capacitance and resistance of coil is ",round(C,2),"micro F and",R,"ohms respectively"

Capacitance and resistance of coil is  1.27 micro F and 15.7 ohms respectively