#Question:
"""Finding the current i(0+)=I0."""
#Variable Declaration:
V=24 #Supply voltage(in Volts)
#Calculations:
Req=20+(1.0/((1.0/20)+(1.0/10)))
I=V/Req
I_L=I*(20.0/(20+10))
Io=I_L
i_0_plus=Io
R=20
v_R=(-Io)*R
R1=(20+10)
v_L=Io*R1
#Result:
print "(a)The current i(0+)=Io=%.2f A." %(i_0_plus)
print "(b)The magnitude of v_R across the 20 Ohms resistor at the instant just after the switch is opened is %.2f V." %(v_R)
print "(c)The magnitude of v_L across the inductor immediately after the switch is opened is %.2f V." %(v_L)
#Question:
"""Finding i(0),the power being absorbed by the inductor at t=1 s."""
from math import e,pow,sqrt,log
#Variable Declaration:
L=1.6 #Self-inductance of the inductor(in Henry)
R=0.8 #Resistance of the resistor(in Ohms)
t=-1.0 #Instant of time(in seconds)
i_minus_1=20.0 #Current at t=1 seconds(in Amperes)
#Calculations:
time_const=L/R
Io=i_minus_1/pow(e,(-t/time_const))
t=1
i_t=Io*pow(e,(-t/time_const))
p_t=i_t*i_t*R
W=100.0
i_t1=sqrt((2*W)/L)
t=-(log(i_t1/Io))*time_const
#Result:
print "(a)i(0) = %.3f A." %(Io)
print "(b)The power absorbed by the resistor is %.2f W. " %(p_t)
print " The inductor by virtue of the emf induced in it,supplies this power to the resistor."
print " Therefore,the power absorbed by the inductor is %.2f W." %(-p_t)
print "(c)The time at which the energy stored in the inductor is 100J is %.5f seconds." %(t)
#Question:
"""Finding the value of current in the circuit at an instant 0.4 s after the switch has been closed."""
from math import e,pow,log
#Variable Declaration:
L=14.0 #Self-inductance of the inductor(in Henry)
R=10.0 #Resistance of the resistor(in Ohms)
V=140.0 #Supply Voltage(in Volts)
#Calculations:
time_const=L/R
t=0.4
Io=V/R
i=Io*(1-pow(e,(-t/time_const)))
i_t=8
t=-time_const*log(i_t/Io)
#Result:
print "(a)The value of current in the circuit at an instant 0.4 s after the switch has been closed is %.3f A." %(i)
print "(b)The time taken for the current to drop to 8 A after the switch is opened is %.4f seconds." %(t)
#Question:
"""Finding the magnitude of the inductor current at t=0- and at t=0+."""
from math import pow,e
#Variable Declaration:
L=40e-03 #Self-inductance of the inductor(in Henry)
R=80.0 #Resistance of the resistor(in Ohm)
V1=20.0 #Supply voltage-1(in Volts)
V2=40.0 #Supply voltage-2(in Volts)
#Calculations:
time_const=L/R
I_01=V1/R
i_0_minus=I_01
i_0_plus=I_01
I_02=(V1+V2)/R
t=1e-03
i_t=I_01+(I_02-I_01)*(1-pow(e,(-t/time_const)))
#Result:
print "(a)The magnitude of inductor current at t=0- is %.2f A." %(i_0_minus)
print "(b)The magnitude of inductor current at t=0+ is %.2f A." %(i_0_plus)
print "(c)As t tends to infinity,the current approaches its final steady-state value given as %.2f A." %(I_02)
print "(d)The magnitude of inductor current at t=1 ms is %.3f A." %(i_t)
#Question:
"""Finding i_L(0-),i2(0-),i_L(0+),i_L(20 ms) and i_2(20 ms)."""
from math import e,pow
#Variable Declaration:
V=20.0 #Source Voltage(in Volts)
R1=20.0 #Resistance of resistor-1(in Ohms)
R2=40.0 #Resistance of resistor-2(in Ohms)
R3=30.0 #Resistance of resistor-3(in Ohms)
R4=25.0 #Resistance of resistor-4(in Ohms)
R5=5.0 #Resistance of resistor-5(in Ohms)
L=2.0 #Self-inductance of inductor(in Henry)
#Calculations:
Io=V/(R4+R5)
i_L_0_minus=Io
i_2_0_minus=V/R3
i_L_0_plus=Io
R_45=R4+R5
R_12=R1+R2
Req=R_45+(1/((1/R_12)+(1/R3)))
time_const=L/Req
t=20e-03
i_L_t=Io*pow(e,(-t/time_const))
i_2_t=-i_L_t*(R_12/(R_12+R3))
#Result:
print "(a)i_L(0-) = %.3f A." %(i_L_0_minus)
print "(b)i_2(0-) = %.3f A." %(i_2_0_minus)
print "(c)i_L(0+) = %.3f A." %(i_L_0_plus)
print "(d)i_L(20 ms) = %.3f A." %(i_L_t)
print "(e)i_2(20 ms) = %.3f A." %(i_2_t)
#Question:
"""Finding v(0+),i(0+) and time constant."""
from math import e,pow
#Variable Declaration:
R=1.5e03 #Resistance of the resistor(in Ohms)
C=5e-06 #Capacitance of the capacitor(in Farad)
Vo=3.0 #Source Voltage(in Volts)
v_0_plus=0 #Voltage across capacitor at t=0+(in Volts)
v_0_minus=0 #Voltage across capacitor at t=0-(in Volts)
#Calculations:
Io=Vo/R
i_0_plus=Io
time_const=R*C
t=15e-03
v=Vo*(1-pow(e,(-t/time_const)))
i=Io*pow(e,(-t/time_const))
#Result:
print "(a)Since the voltage across a capacitor cannot change instantaneously, we have, v(0+)=%d V." %(v_0_plus)
print "(b)i(0+)= %.3f mA." %(i_0_plus*1000)
print "(c)The time constant is %.2f ms." %(time_const*1000)
print "(d)At t=15 ms, \n v=%.5f V. \n i=%.4f mA." %(v,(i*1000))
#Question:
"""Finding v(0+),i(0+) and time constant."""
from math import e,pow
#Variable Declaration:
R=100 #Resistance of the resistor(in Ohms)
C=5e-06 #Capacitance of the capacitor(in Farads)
Vo=3.0 #Source Voltage(in Volts)
#Calculations:
v_0_plus=Vo
v_0_minus=Vo
Io=Vo/R
i_0_plus=-Io
time_const=R*C
t=1.2e-03
v=Vo*pow(e,(-t/time_const))
i=-Io*pow(e,(-t/time_const))
#Result:
print "(a)Since the voltage across a capacitor cannot change instantaneously, we have, v(0+)=%d V." %(v_0_plus)
print "(b)At t=0+, the capacitor behaves as a voltage source of emf Vo. Hence, i(0+)= -Io = %.3f mA." %(i_0_plus*1000)
print "(c) The time constant is %.2f ms." %(time_const*1000)
print "(d)At t=1.2 ms, \n v=%.5f V. \n i=%.4f mA." %(v,(i*1000))
#Question:
"""Finding the current i(t) for t>0 seconds."""
#Calculations:
""" R_Th=(1+10)kilo ohm || (1 kiloohm) """ #Thevenin's Equivalent Resistance(in Ohms)
print("Note: All currents expressed in mA \n")
R_Th=1.0/((1.0/11000)+(1.0/1000))
C=10e-06
time_const=R_Th*C
v_C_0_minus=30.0*((1e03)/((1e03)+(1e03)))
""" Applying KVL, 30-(i_0_plus*(1 kilo ohm))-15=0 """
i_0_plus=(30-15)/1.0
i_infinity=30.0/(1+1+10)
#Result:
print "i(t)= (%.1f + (%.1f-%.1f)*(e to the power -t/%.2f ms)) mA." %(i_infinity,i_0_plus,i_infinity,(time_const*1000))
#Question:
"""Finding the current at t=1 seconds."""
from math import exp,log
#Variable Declaration:
R=3.0 #Resistance of the coil(in Ohms)
time_const=1.8 #Time constant of the coil(in seconds)
V=10.0 #Supply voltage(in Volts)
#Calculations:
L=time_const*R
i_0_plus=0
I0=V/R
i=I0*(1-exp((-1/time_const)))
t=(log(0.5,e))*(-1.8)
growth=V/L
#Result:
print "(a)The current at t=1 seconds is given as %.2f A." %(i)
print "(b)The time at which current attains half of its final value is %.2f seconds." %(t)
print "(c)The initial rate of growth of current is %.2f A/s." %(growth)
#Question:
"""Finding the value of current during a sudden change."""
#Calculations:
"""If I0 is the final steady-state value of current,at t=1 s, we have
i=Io*(1-exp(-1/time_const)) or (0.741*Io)=Io*(1-exp(-1/time_const));
exp(-1/time_const)=0.259;
During the decay of current,we have i(t)=Io*exp(-1/time_const);
Therefore, at t=1s, we have
i1=0.259*Io.
Therefore the value of current in the circuit is 0.259 times the steady state value."""
k=1-0.741
#Result:
print "The value of current in the circuit is %.3f times the steady state value." %(k)
#Question:
"""Finding the current in the circuit at t=0.6 s."""
#Variable Declaration:
V=120.0 #Supply dc voltage(in Volts)
R=20.0 #Resistance of the resistor(in Ohms)
L=8.0 #Inductance of the inductor(in Henry)
#Calculations:
time_const=L/R
Io=V/R
i=Io*(1-exp(-0.6/time_const))
"""The voltage drop across R,v_R=i*r=Io*(1-exp(-t/time_const))*R;
The voltage drop across L,v_L=L*(di/dt)=((L*Io)/time_const)*exp(-t/time_const);
We are to find the time at which these two voltage-drops are same. """
t=-time_const*log(0.5,e)
#Result:
print "(a)The current in the circuit at t=0.6 s is %.2f A." %(i)
print "(b)The time at which the voltage drops across R and L are same is %.3f s." %(t)
#Question:
"""Finding the energy stored in the magnetic field."""
#Variable Declaration:
V=30.0 #Supply dc voltage(in Volts)
R=12.0 #Resistance of the resistor(in Ohms)
L=18.0 #Inductance of the inductor(in Henry)
#Calculations:
time_const=L/R
rate_curr=V/L
Io=V/R
i1=(V/R)*(1-exp(-3.0/time_const))
W1=0.5*i1*i1*L
Wlost=(0.5*L*Io*Io)-W1
#Result:
print "(a)The time constant is %.2f seconds." %(time_const)
print "(b)The initial rate of change of current is %.3f A/s." %(rate_curr)
print "(c)The current at t=3 s is %.2f A." %(i1)
print "(d)The energy stored in the magnetic field at t=3 s is %.3f J." %(W1)
print "(e)The energy lost as heat till t=3 s is %.3f J." %(Wlost)
#Question:
"""Finding the voltage and current at different time instants."""
#Variable Declaration:
R1=200.0 #Resistance of resistor 1(in Ohms)
L=5e-03 #Inductance of the coil(in Henry)
R2=17.0 #Resistance of resistor 2(in Ohms)
#Calculations:
i_0_plus=20e-03
v_0_plus=i_0_plus*R2
time_const=L/R1
v_L_0_plus=(L*i_0_plus)/time_const
t=20e-06
i_20=i_0_plus*exp(-t/time_const)
v_20=v_0_plus
t=50e-06
i_50=i_0_plus*exp(-t/time_const)
v_50=v_0_plus
#Result:
print "(a)The value of i(0+)=%e A." %(i_0_plus)
print "(b)The value of v(0+)=%.3f V." %(v_0_plus)
print "(c)The value of v_L(0+)=%.3f V." %(v_L_0_plus)
print "(d)The value of i at t=20 micro seconds is %e A and v=%.3f V." %(i_20,v_20)
print "(d)The value of i at t=50 micro seconds is %e A and v=%.3f V." %(i_50,v_50)
#Question:
"""Finding the currents at t=5 mill seconds."""
#Variable Declaration:
L=0.8 #Self Inductance of the coil(in Henry)
#Calculations:
i_L_0_minus=(120e-03)*(200.0/(200.0+40.0))
Req=40+(1.0/((1.0/800.0)+(1.0/200.0)))
time_const=L/Req
t=5e-03
i_L=i_L_0_minus*exp(-t/time_const)
i_x=-i_L*(800.0/(800.0+200.0))
i_y=(120e-03)+(-i_L*(200.0/(200.0+800.0)))
#Result:
print "At t=5 milli seconds,"
print "(a)The current i_L=%e A." %(i_L)
print "(b)The current i_x=%e A." %(i_x)
print "(c)The current i_y=%e A." %(i_y)
#Question:
"""Finding the current through an inductor at the time of switching."""
#Variable Declaration:
L=4.0 #Self inductance of inductor(in Henry)
R=10.0 #Resistance of resistor parallel to the inductor(in Ohms)
#Calculations:
"""By superposition theorem, I_L_0=I_L_1+I_L_2; """
I_L1=12.0/4.0
I_L2=2.0
I_L0=I_L1+I_L2
i_L_0_plus=I_L0
w_L_0_plus=0.5*L*I_L0*I_L0
time_const=L/R
t=1.0
i_L=I_L0*exp(-t/time_const)
v_10=-i_L*R
#Result:
print "(a)The current i_L(0+)=%.2f A. The energy stored in the inductor is w_L(0+)=%.2f J." %(i_L_0_plus,w_L_0_plus)
print "(b)At t=1 second, the current in the inductance is %.2f A and the voltage v_10=%.2f V." %(i_L,v_10)
#Question:
"""Finding the energy stored in the inductor."""
#Variable Declaration:
L=5e-03 #Self inductance of inductor(in Henry)
R=200.0 #Resistance of resistor(in Ohms)
#Calculations:
I_L0=5e-03
time_const=L/R
t=20e-06
i_L=I_L0*exp(-t/time_const)
w=0.5*L*i_L*i_L
#Result:
print "The energy stored in the inductor after 20 micro seconds of throwing the switch is %e J." %(w)
#Question:
"""Finding the current in the circuit."""
#Variable DEclaration:
L=8.0 #Self inductance of the coil(in Henry)
R=20.0 #Resistance of resistor(in Ohms)
V=120.0 #Voltage of the supply(in Volts)
#Calculations:
Io=V/R
time_const=L/R
t=0.6
i_t=Io*(1-exp(-t/time_const))
""" The voltage of R at any time is given as v_R(t)=6*(1-exp(-t/0.4))*20=120*(1-exp(-t/0.4));
The voltage across L at any time is v_L(t)=L*(di/dt)=120*exp(-t/0.4);
Applying v_L(t)=v_R(t), """
t=-log(120.0/240.0)*0.4
#Result:
print "(a)The current in the circuit at t=0.6 seconds is %.2f A." %(i_t)
print "(b)The time at which the voltage drops across R and L are same is %.4f seconds."%(t)
#Question:
"""Finding the current i_x in the circuit at different time instants."""
#Variable Declaration:
L=25e-03 #Self inductance of the coil(in Henry)
#Calculations:
I_L0=(10e-03)*(80.0/(80.0+20.0))
i_x_minus_2=I_L0
i_x_0_minus=I_L0
i_x_0_plus=I_L0*(30.0/(30.0+20.0))
Req=1.0/((1.0/20.0)+(1.0/30.0))
time_const=L/Req
t=2e-03
i_L_2=I_L0*exp(-t/time_const)
i_x_2=i_L_2*(30.0/(30.0+20.0))
t=4e-03
i_L_4=I_L0*exp(-t/time_const)
i_x_4=i_L_4*(30.0/(30.0+20.0))
#Result:
print "The current i_x:"
print "At t=-2 ms, i_x=%e A." %(i_x_minus_2)
print "At t=0- ms, i_x=%e A." %(i_x_0_minus)
print "At t=0+ ms, i_x=%e A." %(i_x_0_plus)
print "At t=2 ms, i_x=%e A." %(i_x_2)
print "At t=4 ms, i_x=%e A." %(i_x_4)
#Question:
"""Finding the current and voltage at the time of switching."""
#Variable Declaration:
V=1.5 #Voltage of the supply(in Volts)
R1=5e-03 #Resistance of resistor 1(in Ohms)
R2=1.5e03 #Resistance of resistor 2(in Ohms)
#Calculations:
"""Before the switch is thrown from a to b,the capacitor is fully charged to supply voltage.
When switching takes place,the capacitor starts discharging through the 5 milli Ohms resistance."""
V0=V
v_0_plus=V0
i_0_plus=V0/R1
#Result:
print "The voltage v(0+)=%.2f V and the current i(0+)=%.2f A." %(v_0_plus,i_0_plus)
#Question:
"""Finding the voltage and current at different time intervals."""
#Variable Declaration:
C=5e-06 #Capacitance of the capacitor(in Farads)
V=6.0 #Voltage of the supply(in Volts)
#Calculations:
v_0_minus=6.0*((3.0+2.0)/(3.0+2.0+1.0))
R=(1e03+3e03+2e03)
i_0_minus=V/R
v_0_plus=v_0_minus
Vo=v_0_plus
Req=(5e03+3e03+2e03)
time_const=Req*C
i_0_plus=v_0_plus/Req
Io=i_0_plus
t=0.05
v_t1=Vo*exp(-t/time_const)
i_t1=Io*exp(-t/time_const)
t=0.10
v_t2=Vo*exp(-t/time_const)
i_t2=Io*exp(-t/time_const)
#Result:
print "The values of v(t) and i(t) are: "
print "At t=0- s, v(t)=%.3f V and i(t)=%e A." %(v_0_minus,i_0_minus)
print "At t=0+ s, v(t)=%.3f V and i(t)=%e A." %(v_0_plus,i_0_plus)
print "At t=0.05 s, v(t)=%.3f V and i(t)=%e A." %(v_t1,i_t1)
print "At t=0.10 s, v(t)=%.3f V and i(t)=%e A." %(v_t2,i_t2)
#Question:
"""Finding the voltage and current at the time of switching."""
#Calculations:
"""Using current divider rule, the current through branch AB is determined."""
I_AB=10e-03*(1000.0/(1000.0+(800.0+200.0)))
v_0_minus=I_AB*800.0
V_AB=v_0_minus
v_0_plus=V_AB
i_C_0_plus=V_AB/(1.0/((1.0/200.0)+(1.0/800.0)))
i_0_plus=i_C_0_plus*(800.0/(800.0+200.0))
#Result:
print "The value of v(0+)=%.2f V and the current i(0+)=%e A." %(v_0_plus,i_0_plus)
#Question:
"""Finding the voltages across resistor,capacitor and switch."""
#Variable Declaration:
V=12.0 #Voltage of the supply(in Volts)
C=50e-03 #Capacitance of the capacitor(in Farads)
#Calculations:
v_C_0_minus=12.0*(20.0/(20.0+4.0))
v_C_0_plus=v_C_0_minus
Vo=v_C_0_plus
Req=5.0+20.0
time_const=Req*C
t=1.0
v_C1=Vo*exp(-t/time_const)
v_R1=v_C1*(20.0/(20.0+5.0))
v_SW1=V-V_R1
#Result:
print "The value of v_C at t=1 second is %.3f V." %(v_C1)
print "The value of v_R at t=1 second is %.3f V." %(v_R1)
print "The value of v_SW at t=1 second is %.3f V." %(v_SW1)