# Circuits

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Introduction/Kirchhoff'’s Rules

There are two basic principles of circuitry that can be used to analyze most electrical circuits. They are called
Kirchhoff’s rules.

1. Kirchhoff’s Junction rule (or current rule): The sum of the currents entering any circuit junction is equal to the sum
of the currents leaving the junction. For example, if we apply the rule to the parallel circuit in Figure 1, we get:

I= I1 + I2 + I3

2. Kirchhoff’s Loop rule: The sum of the changes in potential across all elements around any closed circuit loop is
equal to zero, with the conventions that traversing an emf from (-) to (+) results in a positive potential change and
resistors traversed in the direction of the current result in a negative potential change. For example, if we apply
the rule to the series circuit in Figure 1, we get:

V = V1 + V2 + V3 = IR1 + IR2 + IR3

The first rule is a consequence of the conservation of charge. In a circuit, electrons cannot be created nor destroyed.
If a current comes to a juncture, the total amount of electrons going into the juncture must be equal to the total
number of electrons leaving the juncture.

The second is a consequence of the law of conservation of energy. We have learned when dealing with gravity, that if
a hiking path leads you back to the original starting point there is no net change in gravitational potential energy.
Similarly in a circuit, a path that leads back to the starting point results in no in change in electrical potential energy.

Series and Parallel

•   Resistors (or any other device) R1 and R2 are in series if and only if
every loop that contains R1 also contains R2
•   Resistors (or any other device) R1 and R2 are in parallel if and only if you
can find a loop that has ONLY R1 and R2

Use of Meters Reminder

When measuring current with an ammeter, the ammeter should be placed in
series with the device we want to measure the current through. The ammeter
becomes an integral part of the circuit, for example, if we want to measure the               I
current through R1, we place the ammeter in series with R1. On the other                          A
R2
hand, if we want to measure voltage, we just have to connect the voltmeter in
parallel with the device you want to measure the voltage across. For example,        E                R1         R3       V
as shown in the Figure, if we want to measure the voltage across R3, we place
the voltmeter in parallel with R3.

Procedure
Lighting the Light Bulb:

Your first task is to light up one light bulb by using just one light bulb, two conducting wires and a battery (with battery
holder). Draw a diagram of what you did:
Lighting the bulb with one less Wire:
Your task now is to light up one light bulb by using just one light bulb, but just one conducting wire and a battery (no
battery holder). Draw a diagram of what you did:

From the two experiments that you have just completed, explain what is necessary for lighting up the bulb:

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From an energy stand point, what is the role of the battery in the circuit?

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From an energy stand point, what is the role of the wires in the circuit?

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From an energy stand point, what is the role of the color of the wires used in the circuit?

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From an energy stand point, what is the role of the light bulb in the circuit in the circuit?

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From a charge stand point, what is the role of the battery in the circuit?

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From a charge stand point, what is the role of the wires in the circuit?

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From a charge stand point, what is the role of the light bulb in the circuit in the circuit?

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Two Light Bulbs:

In this task, you need to light up two light bulbs. You are allowed to use as much wire as you need and lamp sockets.
There should be two different methods for lighting up the bulbs, series and parallel. Connect two identical light bulbs
in series. How do the light coming off the light bulbs compare?

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Measure the voltage across each of the light bulbs, how do the voltages compare?

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How do you think the currents through both bulbs compare? Explain.

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Unscrew one of the light bulbs? Describe and explain what happens. Precise whether the light intensity in the
remaining bulb changes.

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Connect now two different bulbs in series. How do the light coming off the light bulbs compare?

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Measure the voltage across each of the light bulbs, how do the voltages compare?

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How do you think the currents through both bulbs compare? Explain.

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Now, connect two identical light bulbs in parallel. How do the light coming off the light bulbs compare?

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Measure the current through each of the light bulbs, how do the currents compare?

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How do you think the voltages across both bulbs compare? Explain.

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Unscrew one of the light bulbs? Describe and explain what happens. Precise whether the light intensity in the
remaining bulb changes.

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Connect now two different bulbs in parallel. How do the light coming off the light bulbs compare?

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Measure the current through each of the light bulbs, how do the currents compare?

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How do you think the voltages across both bulbs compare? Explain.

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From your observations, in which configuration did the light bulbs give off more light?

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In which configuration did the light bulbs use more energy?

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From these observations, how do you think your house is wired, is it in series or in parallel? Explain why.

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What about a power strip or extension cord, how is wired, is it in series or in parallel? Explain.

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One Light Bulb – Two Batteries:

In this task, you need to light up one light bulb while using two batteries. You are allowed to use as much wire as you
need and a lamp socket. There should be two different methods for connecting the batteries, series and parallel.
Connect two batteries in series. How do the light coming off the light bulb compare to the time you used only one
battery? How do you think the currents through the bulb compare to using just one battery? Explain

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What did the addition of the battery do to the voltage across the bulb? Explain.

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Connect now two batteries in parellel. How do the light coming off the light bulb compare to the time you used only
one battery? How do you think the currents through the bulb compare to using just one battery? Explain

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What did the addition of the battery do to the voltage across the bulb? Explain.

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In which battery configuration did the light bulb use more energy?

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What would be the purpose of connecting batteries in parallel?

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More Bulbs:

Complete the circuit shown in the figure. A, B and C are identical bulbs; D is different
from F. Identify which bulbs are in series and which bulbs are in parallel.

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Explain why some bulbs are lit and others are not.

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Unscrew bulb B, explain what you see.

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Replace B then unscrew bulb F, explain what you see. How would unscrewing D be different?

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Replace all bulbs then unscrew B and D. Explain what you see.

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Replace all bulbs then measure the current through each of the bulbs (be careful to record the sign) and relate IA, IB
and IC through Kirchhoff’s Junction rule.

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Relate IA, ID and IF through Kirchhoff’s Junction rule.

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Measure the voltages across each of the bulbs and find a relationship between E1, E2, VA, VB and VD.

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Find a relationship between VB, VC, VF and VD.

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Connect point X to point Y in the circuit with a single wire. Explain what happens. If you cannot observe any change in
the bulb lighting, trying to individually unscrew B, C, D, and F.

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Replace the wire between points X and Y by a capacitor. Explain what happens. If you cannot observe any change in
the bulb lighting, trying to individually unscrew B, C, D, and F.

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Consider this new circuit. A, B and C are identical bulbs; D is different from
F. Identify which bulbs are in series and which bulbs or combination of bulbs
are in parallel.

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