Announcements Kirchhoﬀ’s Rules Combinations of Resistors Final Questions

DC Circuits

Sections 19.1 - 19.2

DC Circuits

Announcements

Kirchhoﬀ’s Rules Combinations of Resistors Final Questions

Reading Assignment

Read sections 19.3 - 19.4

Homework Assignment 3

Homework for Chapter 18 is due in class today

Homework Assignment 4

Homework for Chapter 19 (due at the beginning of class on Wednesday,September 22)

Q:1,4,7,19,22

P:2,8,26,32,38,52

DC Circuits

Announcements

Kirchhoﬀ’s Rules

Combinations of Resistors Final Questions

Kirchhoﬀ’s junction rule

At any

junction,the sum of the currents must equal zero

junction

I = 0

Currents directed into the junction are denoted as +I

Currents directed out of a junction are denoted as −I

In other words...

This rule simply states that for a steady ﬂow of charge,there is neither a build-up nor a depletion of charge at any

junction

DC Circuits

Announcements

Kirchhoﬀ’s Rules

Combinations of Resistors Final Questions

Kirchhoﬀ’s junction rule

At any

junction,the sum of the currents must equal zero

junction

I = 0

Currents directed into the junction are denoted as +I

Currents directed out of a junction are denoted as −I

In other words...

This rule simply states that for a steady ﬂow of charge,there is neither a build-up nor a depletion of charge at any

junction

Kirchhoﬀ’s loop rule

The sum of the potential diﬀerences across all circuit elements around any

closed circuit loop must be zero

closed loop

ΔV = 0

What does this mean?

Kirchhoﬀ’s loop rule is simply a statement of conservation of energy!

DC Circuits

Announcements

Kirchhoﬀ’s Rules

Combinations of Resistors Final Questions

Electromotive force

The electromotive force (emf) ε of a battery is the maximum possible voltage the battery can provide

between its terminals

Though its name implies that it is a force,emf is actually a potential diﬀerence (measured in volts)

Using Kirchhoﬀ’s rules

Label the current and the current direction in each branch (just guess a direction if you don’t know for sure)

Use Kirchhoﬀ’s junction rule to write down a current equation for each junction that gives you a diﬀerent

equation (every junction in the circuit except one)

Use Kirchhoﬀ’s loop rule to write down loop equations for as many loops as it takes to obtain,in

combination with the equations from the junction rule,as many equations as there are unknowns

Charges move from a high-potential to a low-potential,so if a resistor is traversed in the direction

of the current,the potential diﬀerence is denoted as −IR

If the resistor is traversed in the direction opposite the current,the potential diﬀerence is denoted

as +IR

If a source of emf (with no internal resistance) is traversed in the direction of the emf (from

negative to positive),the potential diﬀerence is denoted as +ε

If a source of emf (with no internal resistance) is traversed in the direction opposite the emf (from

positive to negative),the potential diﬀerence is denoted as −ε

DC Circuits

Announcements Kirchhoﬀ’s Rules

Combinations of Resistors

Final Questions

Resistors

A resistor is an electronic component that impedes the ﬂow of electric current,converting some of its

energy into heat

When charge ﬂows through a resistor,it experiences a drop

in electric potential given by

ΔV = IR

The power delivered to the resistor by the current is

P = I ΔV = I

2

R =

(ΔV)

2

R

DC Circuits

Announcements Kirchhoﬀ’s Rules

Combinations of Resistors

Final Questions

Resistors

A resistor is an electronic component that impedes the ﬂow of electric current,converting some of its

energy into heat

When charge ﬂows through a resistor,it experiences a drop

in electric potential given by

ΔV = IR

The power delivered to the resistor by the current is

P = I ΔV = I

2

R =

(ΔV)

2

R

Internal resistance

Due to internal resistance in the battery,the actual potential diﬀerence between a battery’s terminals (the so-called

terminal voltage) is less than ε

DC Circuits

Announcements Kirchhoﬀ’s Rules

Combinations of Resistors

Final Questions

Series combination

DC Circuits

Announcements Kirchhoﬀ’s Rules

Combinations of Resistors

Final Questions

Series combination

The current through each resistor is the same (I

1

= I

2

= I ) (why?)

The total potential diﬀerence ΔV

tot

across resistors connected in series is the sum of the potential

diﬀerences across the individual resistors (ΔV

tot

= ΔV

1

+ ΔV

2

+...)

The equivalent resistance is the algebraic sum of the individual resistances

R

eq

= R

1

+ R

2

+ R

3

+...

Therefore,the equivalent resistance of a series combination of resistors is always greater than any

individual resistance

DC Circuits

Announcements Kirchhoﬀ’s Rules

Combinations of Resistors

Final Questions

Parallel combination

DC Circuits

Announcements Kirchhoﬀ’s Rules

Combinations of Resistors

Final Questions

Series combination

The current through each resistor is the same (I

1

= I

2

= I ) (why?)

The total potential diﬀerence ΔV

tot

across resistors connected in series is the sum of the potential

diﬀerences across the individual resistors (ΔV

tot

= ΔV

1

+ ΔV

2

+...)

The equivalent resistance is the algebraic sum of the individual resistances

R

eq

= R

1

+ R

2

+ R

3

+...

Therefore,the equivalent resistance of a series combination of resistors is always greater than any

individual resistance

Parallel combination

The potential diﬀerence across each resistor is the same (ΔV

1

= ΔV

2

= V) (why?)

The total current I is the sum of the currents across the individual resistors (I = I

1

+ I

2

+...)

The inverse of the equivalent resistance is the algebraic sum of the inverses of the individual resistances

1

R

eq

=

1

R

1

+

1

R

2

+

1

R

3

+...

Therefore,the equivalent resistance of a parallel combination of resistors is always less than the smallest

individual resistance in the group

DC Circuits

Announcements Kirchhoﬀ’s Rules

Combinations of Resistors

Final Questions

Scenario

Two lightbulbs are connected in series to a power source.Treat a lightbulb as an example of a resistor.

DC Circuits

Announcements Kirchhoﬀ’s Rules

Combinations of Resistors

Final Questions

Scenario

Two lightbulbs are connected in series to a power source.Treat a lightbulb as an example of a resistor.

Question#1

If the ﬁlament of the ﬁrst lightbulb fails,what would happen to the second lightbulb?

DC Circuits

Announcements Kirchhoﬀ’s Rules

Combinations of Resistors

Final Questions

Scenario

Two lightbulbs are connected in series to a power source.Treat a lightbulb as an example of a resistor.

Question#1

If the ﬁlament of the ﬁrst lightbulb fails,what would happen to the second lightbulb?

Answer

It would go out

DC Circuits

Announcements Kirchhoﬀ’s Rules

Combinations of Resistors

Final Questions

Scenario

Two lightbulbs are connected in series to a power source.Treat a lightbulb as an example of a resistor.

Question#1

If the ﬁlament of the ﬁrst lightbulb fails,what would happen to the second lightbulb?

Answer

It would go out

Question#2

If the ﬁlament of the second lightbulb fails,what would happen to the ﬁrst lightbulb?

DC Circuits

Announcements Kirchhoﬀ’s Rules

Combinations of Resistors

Final Questions

Scenario

Two lightbulbs are connected in series to a power source.Treat a lightbulb as an example of a resistor.

Question#1

If the ﬁlament of the ﬁrst lightbulb fails,what would happen to the second lightbulb?

Answer

It would go out

Question#2

If the ﬁlament of the second lightbulb fails,what would happen to the ﬁrst lightbulb?

Answer

It would go out

DC Circuits

Announcements Kirchhoﬀ’s Rules Combinations of Resistors

Final Questions

Reading Assignment

Read sections 19.3 - 19.4

Homework Assignment 3

Homework for Chapter 18 is due in class today

Homework Assignment 4

Homework for Chapter 19 (due at the beginning of class on Wednesday,September 22)

Q:1,4,7,19,22

P:2,8,26,32,38,52

DC Circuits

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