Chapter 4 : Series Circuits

Example No. 4_1 Page No. 117

In [1]:
# Two resistances R1 and R2 of 5 Ohms each and R3 of 10 Ohms are in series. How much is Rt?

# Given data

R1 = 5#     # Resistor 1=5 Ohms
R2 = 5#     # Resistor 2=5 Ohms
R3 = 10#    # Resistor 3=10 Ohms

Rt = R1+R2+R3#
print 'The Combined Series Resistance = %0.f Ohms'%Rt

The Combined Series Resistance = 20 Ohms

Example No. 4_2 Page No. 117

In [2]:
#With 80 V applied across the series string, how much is the current in R3?

# Given data

Rt = 20#     # Total Resistance=20 Ohms
Vt = 80#     # Applied Voltage=80 Volts

I = Vt/Rt#
print 'The Current in Resistor R3 connected in Series = %0.f Amps'%I

The Current in Resistor R3 connected in Series = 4 Amps

Example No. 4_3 Page No. 119

In [5]:
# Solve for Rt, I and the individual resistor voltage drops at R1, R2, R3.

# Given data

R1 = 10.#     # Resistor 1=10 Ohms
R2 = 20.#     # Resistor 2=20 Ohms
R3 = 30.#     # Resistor 3=30 Ohms
Vt = 12.0#     # Applied Voltage=12 Volts

Rt = R1+R2+R3#
print 'The combined series resistance = %0.f ohms'%Rt

I = Vt/Rt#
print 'The current = %0.2f Amps'%I
print 'i.e 200 mA'

V1 = I*R1
print 'The Voltage Drop of Resistor R1 = %0.2f Volts'%V1

V2 = I*R2
print 'The Voltage Drop of Resistor R2 = %0.2f Volts'%V2

V3 = I*R3
print 'The Voltage Drop of Resistor R3 = %0.2f Volts'%V3

The combined series resistance = 60 ohms
The current = 0.20 Amps
i.e 200 mA
The Voltage Drop of Resistor R1 = 2.00 Volts
The Voltage Drop of Resistor R2 = 4.00 Volts
The Voltage Drop of Resistor R3 = 6.00 Volts

Example No. 4_4 Page No. 123

In [7]:
# A voltage source produces an IR drop of 40 V across a 20 Ohms R1, 60 V across a 30 Ohms R2, and 180 V across a 90 Ohms R3, all in series. According to Kirchhoff’s voltage law, how much is the applied voltage Vt ?

# Given data

V1 = 40#     # Voltage drop at R1=40 Volts
V2 = 60#     # Voltage drop at R2=60 Volts
V3 = 180#    # Voltage drop at R3=180 Volts

Vt = V1+V2+V3#
print 'The Applied Voltage Vt = %0.f Volts'%Vt

The Applied Voltage Vt = 280 Volts

Example No. 4_5 Page No. 123

In [8]:
# An applied Vt of 120 V produces IR drops across two series resistors R 1 and R 2 If the voltage drop across R1 is 40 V, how much is the voltage drop across R2?

# Given data

V1 = 40#     # Voltage drop at R1=40 Volts
Vt = 120#    # Applied Voltage=120 Volts

V2 = Vt-V1#
print 'The Voltage Drop across Resistor R2 = %0.f Volts'%V2

The Voltage Drop across Resistor R2 = 80 Volts

Example No. 4_6 Page No. 131

In [10]:
# Assume that the series circuit in Fig. 4–20 has failed. A technician troubleshooting the circuit used a voltmeter to record the following resistor voltage drops. V1=0 V# V2=0 V# V3=24 V# V4=0 V. Based on these voltmeter readings, which component is defective and what type of defect is it? (Assume that only one component is defective.)

# Given data

R1 = 150.#     # Resistor 1=150 Ohms
R2 = 120.#     # Resistor 2=120 Ohms
R3 = 180.#     # Resistor 3=180 Ohms
R4 = 150.#     # Resistor 4=150 Ohms
Vt = 24.#      # Applied Voltage=24 Volts

Rt = R1+R2+R3+R4#

I = Vt/Rt#

V1 = I*R1
print 'The Voltage Drop of Resistor R1 = %0.2f Volts'%V1

V2 = I*R2
print 'The Voltage Drop of Resistor R2 = %0.2f Volts'%V2

V3 = I*R3
print 'The Voltage Drop of Resistor R3 = %0.2f Volts'%V3

V4 = I*R4
print 'The Voltage Drop of Resistor R4 = %0.2f Volts'%V4

print 'The Resistor R3 is defective since it is open circuit and drops all the voltage arround it'

The Voltage Drop of Resistor R1 = 6.00 Volts
The Voltage Drop of Resistor R2 = 4.80 Volts
The Voltage Drop of Resistor R3 = 7.20 Volts
The Voltage Drop of Resistor R4 = 6.00 Volts
The Resistor R3 is defective since it is open circuit and drops all the voltage arround it

Example No. 4_7 Page No. 133

In [12]:
# Assume that the series circuit has failed. A technician troubleshooting the circuit used a voltmeter to record the following resistor voltage drops: V1  8 V#V2  6.4 V#V3  9.6 V#V4  0 V. Based on the voltmeter readings, which component is defective and what type of defect is it? (Assume that only one component is defective.)

# Given data

R1 = 150.#     # Resistor 1=150 Ohms
R2 = 120.#     # Resistor 2=120 Ohms
R3 = 180.#     # Resistor 3=180 Ohms
R4 = 150.#     # Resistor 4=150 Ohms
Vt = 24.#      # Applied Voltage=24 Volts

print 'Calculated from the Circuit'

Rt = R1+R2+R3+R4#

I = Vt/Rt#

V1 = I*R1
print 'The Voltage Drop of Resistor R1 = %0.2f Volts'%V1

V2 = I*R2
print 'The Voltage Drop of Resistor R2 = %0.2f Volts'%V2

V3 = I*R3
print 'The Voltage Drop of Resistor R3 = %0.2f Volts'%V3

V4 = I*R4
print 'The Voltage Drop of Resistor R4 = %0.2f Volts'%V4

Calculated from the Circuit
The Voltage Drop of Resistor R1 = 6.00 Volts
The Voltage Drop of Resistor R2 = 4.80 Volts
The Voltage Drop of Resistor R3 = 7.20 Volts
The Voltage Drop of Resistor R4 = 6.00 Volts