In [1]:

```
from __future__ import division
import math
#from pylab import *
%matplotlib inline
#initializing the variables:
C = 15E-6;# in Farads
R = 47000;# in ohms
V = 120;# in Volts
#calculation:
tou = R*C
t1 = tou
Vctou = V*(1-math.e**(-1*t1/tou))
Vct = V/2
t0 = -1*tou*math.log(1 - Vct/V)
t=[]
Vc=[]
I = V/R
for h in range(50):
t.append((h-1)/10)
k=(h-1)/10
Vc.append(V*(1 - math.e**(-1*k/tou)))
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.plot(t,Vc,'-')
#plot(t,Vc,'-')
xlabel('time(sec)')
ylabel('Volts(V)')
show()
#Results
print "\n\n Result \n\n"
print "\n (a)the capacitor voltage at a time equal to one time constant = ",round(Vctou,2)," V"
print "\n (b)the time for the capacitor voltage to reach one half of its steady state value = ",round(t0,5)," secs"
```

In [8]:

```
from __future__ import division
import math
#from pylab import *
%matplotlib inline
#initializing the variables:
C = 4E-6;# in Farads
R = 220000;# in ohms
V = 24;# in Volts
t1 = 1.5;# in secs
#calculation:
tou = R*C
I = V/R
t=[]
Vc=[]
for h in range(50):
t.append((h-1)/10)
k=(h-1)/10
Vc.append(V*math.e**(-1*k/tou))
#plt.figsize(10,8)
fig = plt.figure()
#canvas = fc(fig)
ax = fig.add_subplot(1, 1, 1)
ax.plot(t,Vc,'-')
#plot(t,Vc,'-')
xlabel('time(sec)')
ylabel('P.D across Capacitor(V)')
show()
t=[]
VR=[]
for h in range(50):
t.append((h-1)/10)
k=(h-1)/10
VR.append(V*(1 - math.e**(-1*k/tou)))
fig = plt.figure()
#canvas = fc(fig)
ax = fig.add_subplot(1, 1, 1)
ax.plot(t,VR,'-')
#plot(t,VR,'-*')
xlabel('time(sec)')
ylabel('P.D across Resistor(V)')
show()
t=[]
i=[]
for h in range(50):
t.append((h-1)/10)
k=(h-1)/10
i.append(I*math.e**(-1*k/tou))
fig = plt.figure()
#canvas = fc(fig)
ax = fig.add_subplot(1, 1, 1)
ax.plot(t,i,'-')
#plot(t,i,'*-')
xlabel('time(sec)')
ylabel('current(A)')
show()
Vct1 = V*math.e**(-1*t1/tou)
VRt1 = V*math.e**(-1*t1/tou)
it1 = I*math.e**(-1*t1/tou)
#Results
print "\n\n Result \n\n"
print "\n the value of capacitor voltage is ",round(Vct1,1)," V, resistor voltage is ",round(VRt1,1)," V,"
print "current is ",round(0.02,2)," mA at one and a half seconds after discharge has started."
```

In [9]:

```
from __future__ import division
import math
#initializing the variables:
C = 20E-6;# in Farads
R = 50000;# in ohms
V = 20;# in Volts
t1 = 1;# in secs
t2 = 2;# in secs
VRt = 15;# in Volts
#calculation:
tou = R*C
I = V/R
Vct1 = V*(1-math.e**(-1*t2/tou))
t3 = -1*tou*math.log(VRt/V)
it1 = I*math.e**(-1*t1/tou)
#Results
print "\n\n Result \n\n"
print "\n (a)initial value of the current flowing is ",round(I*1000,1),"mA"
print "\n (b)time constant of the circuit ",round(tou,2)," Sec"
print "\n (c)the value of the current one second after connection, ",round((it1/1E-3),3)," mA"
print "\n (d)the value of the capacitor voltage two seconds after connection ",round(Vct1,1)," V"
print "\n (e)the time after connection when the resistor voltage is 15 V is ",round(t3,3)," sec"
```

In [10]:

```
from __future__ import division
import math
#initializing the variables:
C = 0.5E-6;# in Farads
V = 10;# in Volts
tou = 0.012;# in secs
t1 = 0.007;# in secs
#calculation:
R = tou/C
Vc = V*(1-math.e**(-1*t1/tou))
#Results
print "\n\n Result \n\n"
print "\n (a)value of the resistor is ",R," ohm"
print "\n (b)capacitor voltage is ",round(Vc,2)," V"
```

In [11]:

```
from __future__ import division
import math
#initializing the variables:
R = 50000;# in ohms
V = 100;# in Volts
Vc1 = 20;# in Volts
tou = 0.8;# in secs
t1 = 0.5;# in secs
t2 = 1;# in secs
#calculation:
C = tou/R
t = -1*tou*math.log(Vc1/V)
I = V/R
it1 = I*math.e**(-1*t1/tou)
Vc = V*math.e**(-1*t2/tou)
#Results
print "\n\n Result \n\n"
print "\n (a)the value of the capacitor is ",round((C/1E-6),2),"uF"
print "\n (b)the time for the capacitor voltage to fall to 20 V is ",round(t,2)," sec"
print "\n (c)the current flowing when the capacitor has been discharging for 0.5 s is ",round(it1*1000,2),"mA"
print "\n (d)voltage drop across resistor when the capacitor has been discharging for one second is ",round(Vc,1)," V"
```

In [12]:

```
from __future__ import division
import math
#initializing the variables:
C = 0.1E-6;# in Farads
R = 4000;# in ohms
V = 200;# in Volts
Vc1 = 2;# in Volts
#calculation:
tou = R*C
I = V/R
t = -1*tou*math.log(Vc1/V)
#Results
print " \n\n Result \n\n"
print "\n (a) initial discharge current is ",round(I,2)," A"
print "\n (b)Time constant tou is ",round(tou,5)," sec"
print "\n (c)min. time required for voltage across capacitor to fall to less than 2 V is ",round(t*1000,0)," msec"
```

In [13]:

```
from __future__ import division
import math
from pylab import *
#initializing the variables:
L = 0.1;# in Henry
R = 20;# in ohms
V = 60;# in Volts
i2 = 1.5;# in Amperes
#calculation:
tou = L/R
t1 = 2*tou
t=[]
i=[]
I = V/R
for h in range(250):
t.append((h-1)/10000)
k=(h-1)/10000
i.append(I*(1 - math.e**(-1*k/tou)))
plot(t,i,'-')
xlabel('time(sec)')
ylabel('current(A)')
show()
i1 = I*(1 - math.e**(-1*t1/tou))
t2 = -1*tou*math.log(1 - i2/I)
#Results
print " \n\n Result \n\n"
print "\n (a) the value of current flowing at a time equal to two time constants is ",round(i1,2)," A"
print "\n (b)the time for the current to grow to 1.5 A is ",round(t2,5)," sec"
```

In [14]:

```
from __future__ import division
import math
#initializing the variables:
L = 0.04;# in Henry
R = 10;# in ohms
V = 120;# in Volts
#calculation:
tou = L/R
t1 = tou
I = V/R
i1 = I*(1 - math.e**(-1*t1/tou))
i2 = 0.01*I
t2 = -1*tou*(-5)
#Results
print "\n\n Result \n\n"
print "\n (a) the final value of current is ",round(I,2)," A"
print "\n (b)time constant of the circuit is ",round(tou*1000,2),"msec"
print "\n (c) value of current after a time equal to the time constant is ",round(i1,2)," A"
print "\n (d)expected time for current to rise to within 0.01 times of its final value is ",round(t2*1000,2),"msec"
```

In [15]:

```
from __future__ import division
import math
#initializing the variables:
L = 3;# in Henry
R = 15;# in ohms
V = 120;# in Volts
t1 = 0.1;# in secs
t3 = 0.3;# in secs
#calculation:
tou = L/R
I = V/R
i2 = 0.85*I;# in amperes
VL = V*math.e**(-1*t1/tou)
t2 = -1*tou*math.log(1 - (i2/I))
i3 = I*(1 - math.e**(-1*t3/tou))
#Results
print "\n\n Results \n\n"
print "\n (a) steady state value of current is ",round(I,2)," A"
print "\n (b)time constant of the circuit is ",round(tou,2)," sec"
print "\n (c)value of the induced e.m.f. after 0.1 s is ",round(VL,2)," V"
print "\n (d) time for the current to rise to 0.85 times of its final values is ",round(t2,2)," A"
print "\n (e)value of the current after 0.3 s is ",round(i3,2)," A"
```

In [16]:

```
from __future__ import division
import math
from pylab import *
#initializing the variables:
R = 15;# in ohms
V = 110;# in Volts
tou = 2;# in secs
t1 = 3;# in secs
i2 = 5;# in amperes
#calculation:
L = tou*R
I = V/R
t=[]
i=[]
for h in range(100):
t.append((h-1)/10)
k=(h-1)/10
i.append(I*math.e**(-1*k/tou))
plot(t,i,'-')
xlabel('time(sec)')
ylabel('current(A)')
show()
i1 = I*(math.e**(-1*t1/tou))
t2 = -1*tou*log((i2/I))
#Results
print " \n\n Result \n\n"
print "\n (a)the current flowing in the winding 3 s after being shorted-out is ",round(i1,2)," A"
print "\n (b)the time for the current to decay to 5 A is ",round(t2,2)," sec"
```

In [17]:

```
from __future__ import division
import math
#initializing the variables:
L = 6;# in Henry
r = 10;# in ohms
V = 120;# in Volts
tou = 0.3;# in secs
t1 = 1;# in secs
#calculation:
R = (L/tou) - r
Rt = R + r
I = V/Rt
i2 = 0.1*I
i1 = I*(math.e**(-1*t1/tou))
t2 = -1*tou*math.log((i2/I))
#Results
print " \n\n Result \n\n"
print "\n (a) resistance of the coil is ",round(R,2)," ohm"
print "\n (b) current flowing in circuit one second after the shorting link has been placed is ",round(i1,2)," A"
print "\n (c)the time for the current to decay to 0.1 times of initial value is ",round(t2,2)," sec"
```

In [18]:

```
from __future__ import division
import math
#initializing the variables:
L = 0.2;# in Henry
R = 1000;# in ohms
V = 24;# in Volts
t1 = 1*L/R;# in secs
t2 = 2*L/R;# in secs
t3 = 3*L/R;# in secs
#calculation:
tou = L/R
I = V/R
i1 = I*(1 - math.e**(-1*t1/tou))
VL = V*(math.e**(-1*t2/tou))
VR = V*(1 - math.e**(-1*t3/tou))
#Results
print "\n\n Result \n\n"
print "\n time constant of circuit is ",round(tou*1000,6),"msec, and steady-state value of current is ",round(I*1000,2),"mA"
print "\n (a) urrent flowing in the circuit at a time equal to one time constant is ",round(i1*1000,2),"mA"
print "\n (b) voltage drop across the inductor at a time equal to two time constants is ",round(VL,3)," V"
print "\n (c)the voltage drop across the resistor after a time equal to three time constants is ",round(VR,2)," V"
```