# 1.1.5 ```Activity 1.1.5a Circuit Theory: Hand Calculations
Introduction
Have you ever used a calculator to add some numbers, looked at the answer, and realized
that it was wrong? How did you know that the answer was incorrect? The calculator gave you
an answer; why did you not trust it? You knew the answer was wrong because you
understand the fundamentals of mathematics. Your instinct told you that the answer could not
be correct.
The same is true for circuit analysis. Throughout this course you will be using Circuit Design
Software (CDS) to test the circuits that you design. This software will always give an answer,
whether it is right or wrong. The only way that you will be able to rely on these answers is if
you have an understanding of the laws of circuit analysis. You must develop the same instinct
for circuit behavior that you have for mathematics.
In this activity you will gain experience applying Ohm’s Law and Kirchhoff’s Voltage and
Current Laws to solve simple series and parallel circuits.
Equipment

Calculator
Procedure
1. For each of the resistors shown below, use Ohm’s Law to calculate the unknown
quantity. Be sure to put your answer in proper engineering notation and use the
correct units.
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Digital Electronics Activity 1.1.5a Circuit Theory: Hand Calculations – Page 1
1.
2.
3.
4.
5.
6.
7.45mA
225.806kΩ
30.8kV
240Ω
2.94mV
300V
2. For each of the circuits shown below, calculate the value for RT.
Be sure to put your answer in proper engineering notation and use the correct units.
Calculations:
a) 2.17kΩ
a)
b)10.9kΩ
b)
c) 564.487Ω
c)
d) 66.7Ω
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Digital Electronics Activity 1.1.5a Circuit Theory: Hand Calculations – Page 2
d)
3. Using the laws of circuit theory, solve for RT, IT, VR1, VR2, &amp; VR3.
Be sure to put your answer in proper engineering notation and use the correct units.
Using the calculations from problem (3), verify your results using Kirchhoff’s Voltage Law.
RT=1.94 kΩ
IT=4.64 mA
VR1= 2.18 V
VR2=5.57 V
VR3=1.25 V
4. Using the laws of circuit theory, solve for RT, IT, VR1, VR2, VR3, &amp; VR4. Be sure to put
Using the calculations from problem (4), verify your results using Kirchhoff’s Voltage La
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Digital Electronics Activity 1.1.5a Circuit Theory: Hand Calculations – Page 3
RT=2.42kΩ
IT=248&micro;A
VR1= 669.6 &micro;V
VR2=2.48mV
VR3=818.4&micro;V
VR4=2.034 mV
5. Using the laws of circuit theory, solve for RT, IT, IR1, IR2, &amp; IR3. Be sure to put your
answer in proper engineering notation and use the correct units.
RT
= 2.08 kΩ
IT
= 5.78 mA
IR1
= 1.46 mA
IR2
= 1.77 mA
IR3
= 2.55 mA
6. Using the laws of circuit theory, solve for RT, IT, IR1, IR2, IR3, &amp; IR4. Be sure to put your
answer in proper engineering notation and use the correct units.
RT
= 1.12 kΩ
IT
= 5.37 mA
IR1
= 2.22 mA
IR2
= 600 μA
IR3
= 1.82 mA
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Digital Electronics Activity 1.1.5a Circuit Theory: Hand Calculations – Page 4
IR4
= 731 μA
Using the calculations from problem (6), verify your results using Kirchhoff’s Current Law.
Conclusion
1. State two rules for the voltage and current in a series circuit.
The current flowing through every series component is equal.
The total resistance (RT) is equal to the sum of all of the resistances (i.e., R1 + R2 + R3).
2. State two rules for the voltage and current in a parallel circuit.
The voltage across every parallel component is equal.
The total resistance (RT) is equal to the reciprocal of the sum of the reciprocal:
The sum of all of the currents in each branch (IR1 + IR2 + IR3) is equal to the total current
(IT). This is called Kirchhoff’s Current Law.
3. If you remove a single bulb from an inexpensive string of Christmas tree lights, all of
the lights in the entire string will go off. Are the bulbs connected in series or parallel?
Explain. Series circuit because they depend on each other to carry the flow of
electricity, If one component goes out, so do all the others.
Going Further – Optional
The circuit shown below is a series/parallel circuit. That is, some of its resistors are
connected in series and some are in parallel. Using the laws of circuit theory,
solve for RT &amp; IT.
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Digital Electronics Activity 1.1.5a Circuit Theory: Hand Calculations – Page 5
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