Chapter 5 : Parallel Circuits

Example No. 5_1 Page No. 149

In [3]:
# Solve for branch currents I1 and I2.

R1 = 1.*10**3#    # Resistor 1=1*10**3 Ohms
R2 = 600.#       # Resistor 2=600 Ohms
Va = 15.#        # Applied Voltage=15 Volts

I1 = Va/R1#
print 'The Current Resistor R1 = %0.3f Amps'%I1
print 'i.e 15 mAmps'

I2 = Va/R2#
print 'The Current Resistor R2 = %0.2f Amps'%I2
print 'i.e 25 mAmps'

The Current Resistor R1 = 0.015 Amps
i.e 15 mAmps
The Current Resistor R2 = 0.03 Amps
i.e 25 mAmps

Example No. 5_2 Page No. 150

In [6]:
# An R1 of 20 Ohms, an R2 of 40 Ohms, and an R3 of 60 Ohms are connected in parallel across the 120-V power line. Using Kirchhoff’s current law, determine the total current It.

# Given data

R1 = 20.#      # Resistor 1=20 Ohms
R2 = 40.#      # Resistor 2=40 Ohms
R3 = 60.#      # Resistor 3=60 Ohms
Va = 120.#     # Applied Voltage=120 Volts

I1 = Va/R1#
I2 = Va/R2#
I3 = Va/R3#

It = I1+I2+I3
print 'The Total Current in the Mainline = %0.f Amps'%It

The Total Current in the Mainline = 11 Amps

Example No. 5_3 Page No. 151

In [7]:
# Two branches R1 and R2 across the 120-V power line draw a total line current It of 15 A. The R1 branch takes 10 A. How much is the current I2 in the R2 branch?

# Given data

I1 = 10#        # Current in R1 branch=10 Amps
It = 15#        # Total Current=15 Amps

I2 = It-I1#
print 'The Current in R2 branch = %0.f Amps'%I2

The Current in R2 branch = 5 Amps

Example No. 5_4 Page No. 152

In [10]:
# Three parallel branch currents are 0.1 A, 500 mA, and 800 A. Using Kirchhoff’s current law, calculate It.


# Given data

I1 = 0.1#              # Branch Current 1=0.1 Amps
I2 = 0.5#              # Branch Current 2=500m Amps
I3 = 800*10**-6#        # Branch Current 3=800u Amps

It = I1+I2+I3#
print 'The Total Current = %0.4f Amps'%It
print 'i.e 600.8 mAmps'

The Total Current = 0.6008 Amps
i.e 600.8 mAmps

Example No. 5_5 Page No. 153

In [11]:
# Two branches, each with a 5-A current, are connected across a 90-V source. How much is the equivalent resistance Req?

# Given data

I1 = 5#      # Branch Current 1=5 Amps
I2 = 5#      # Branch Current 2=5 Amps
Va = 90#     # Applied Voltage=90 Volts

It = I1+I2#
Req = Va/It#
print 'The Equivalent Resistance Req = %0.f Ohms'%Req

The Equivalent Resistance Req = 9 Ohms

Example No. 5_6 Page No. 158

In [13]:
# What Rx in parallel with 40 Ohms will provide an Req of 24 Ohms?

# Given data

R = 40.0#         # Resistance=40 Ohms
Req = 24.0#       # Equivqlent Resistance=24 Ohms

Rx = (R*Req)/(R-Req)#
print 'The Value of Rx = %0.2f Ohms'%Rx

The Value of Rx = 60.00 Ohms

Example No. 5_7 Page No. 158

In [16]:
# What R in parallel with 50 kOhms will provide an Req of 25 kOhms

# Given data

R1 = 50*10**3#         # R1=50k Ohms
Req = 25*10**3#       # Req=25k Ohms

R = (R1*Req)/(R1-Req)#
print 'The value of R = %0.f Ohms'%R
print 'i.e 50 kohms'

The value of R = 50000 Ohms
i.e 50 kohms