physics - giancoli 7e ch 19: dc...

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PHYSICS - GIANCOLI 7E

CH 19: DC CIRCUITS

CONCEPT: COMBINING RESISTORS IN SERIES AND PARALLEL

In Circuit problems, you will need to COLLAPSE / COMBINE resistors into a SINGLE ___________________ resistors.

SERIES CONNECTION PARALLEL CONNECTION

- Direct connection, no splits

- Equivalent Resistance 𝐑𝐞𝐪 = ________________

- Always ___________ than individual resistances

- Wire splits, forms a loop

- Equivalent Resistance 𝐑𝐞𝐪 = ________________

- Always ___________ than individual resistances

EXAMPLE 1: What is the equivalent resistance of the following resistors?

EXAMPLE 2: What is the equivalent resistance of the following resistors?

1 Ω 3 Ω

2 Ω 4 Ω


CH 19: DC CIRCUITS

PRACTICE: EQUIVALENT RESISTANCE #1

What is the equivalent resistance of the following combination of resistors?

1 Ω

2 Ω

3 Ω

4 Ω


CH 19: DC CIRCUITS

CONCEPT: SHORTCUT EQUATIONS FOR RESISTORS IN PARALLEL SHORTCUT #1: If you have TWO resistors in Parallel, you can use: Note this does NOT work if you have more than 2 resistors! SHORTCUT #2: If you have resistors of SAME resistance in Parallel, you can use: EXAMPLE: What is the equivalent resistance of the following network of resistors?

9Ω 12Ω 9Ω 12Ω 9Ω


CH 19: DC CIRCUITS

PRACTICE: EQUIVALENT RESISTANCE #2

What is the equivalent resistance of the following combination of resistors?

EXAMPLE: EQUIVALENT RESISTANCE OF WEIRD ARRANGEMENT What is the equivalent resistance of the following resistors?

A

B

2Ω 3Ω


CH 19: DC CIRCUITS

PRACTICE: EQUIVALENT RESISTANCE WITH VARIABLES If every resistor below has resistance R, what is the equivalent resistance of the combination, in terms of R?


CH 19: DC CIRCUITS

CONCEPT: KIRCHHOFF’S JUNCTION RULE

Remember: Resistors in Series have the same _________________.

- Current changes ONLY IF the wire SPLITS into 2 or more.

- Points where a wire SPLITS are called JUNCTIONS or NODES.

EXAMPLE 1: What is the voltage of the 2 Ω resistor in the following figure? (Remember: V = IR)

Current INTO a junction is always ________________ current OUT of the junction 𝚺𝒊𝒊𝒏 _______ 𝚺𝒊𝒐𝒖𝒕 - This rule is called Kirchhoff’s JUNCTION Rule or Kirchhoff’s _______________ Law.


CH 19: DC CIRCUITS

CONCEPT: SOLVING RESISTOR CIRCUITS In Circuit problems, you will need to find the CURRENT and VOLTAGE of different Resistors.


- Equivalent Resistance:

𝑹𝒆𝒒 = 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑

- Share [ CURRENT / VOLTAGE ] with EACH OTHER

- Share [ CURRENT / VOLTAGE ] with EQUIVALENT Resistor

- Equivalent Resistance:

𝟏/𝐑𝐞𝐪 = 𝟏/𝐑𝟏 + 𝟏/𝐑𝟐 + 𝟏/𝐑𝟑

- Share [ CURRENT / VOLTAGE ] with EACH OTHER

- Share [ CURRENT / VOLTAGE ] with EQUIVALENT Resistor

STEPS for Solving Resistor Circuits:

1) “Collapse” down to ONE EQUIVALENT Resistor

2) Find VOLTAGE and CURRENT on Equivalent Resistor

3) “Work backwards” noting VOLTAGE and CURRENT on EACH Resistor

EXAMPLE: What is the current and voltage of each of the resistors in the following circuit?


CH 19: DC CIRCUITS

PRACTICE: FIND CURRENT & VOLTAGE IN ALL RESISTORS What is current and voltage across each resistor below?


CH 19: DC CIRCUITS

EXAMPLE: FIND CURRENT OF ONE CAPACITOR What is the current on the 3 Ω resistor below?


CH 19: DC CIRCUITS

PRACTICE: FIND VOLTAGE OF THE BATTERY What is the voltage of the battery below?


CH 19: DC CIRCUITS

CONCEPT: INTRODUCTION TO KIRCHHOFF’S LOOP RULE

So far we have only seen SINGLE source circuits. To solve circuits with MULTIPLE sources, we will need new “TOOLS”

For each LOOP in a circuit, we can write one LOOP EQUATION.

- Each equation adds/subtracts voltages of batteries and resistors. - The voltage of resistors is written as _______ (from __________) 𝚺𝑽 = _____________________________ = ______

Each voltage is added or subtracted depending on (1) DIRECTION OF CURRENT, and (2) DIRECTION OF LOOP.

(1) FIRST, use DIRECTION of CURRENT to put +/– signs on the ends of each resistor:

- RESISTOR Positive end is where ________________________ the resistor.

- BATTERY Positive end is positive (longer) terminal (does not depend on direction of current)

(2) SECOND, choose DIRECTION OF LOOP, which is just the sequence in which we will add/subtract voltages. - When “crossing” elements in this direction, you ADD a voltage if you crossed from _______ to _______.

EXAMPLE: Write a Loop Equation for the circuit above (repeated below), but now using the opposite Direction of Loop.

Kirchhoff’s LOOP rule states that the SUM of all the VOLTAGES around a LOOP is ________.

𝚺𝑽 = ________ - This rule is also called Kirchhoff’s _______________ Law. - This works for ANY circuit, but is especially useful for circuits with MULTIPLE sources.

i

R1 V2

R2 V1

i

R1 V2

R2 V1

i

R1 V2

R2 V1


CH 19: DC CIRCUITS

CONCEPT: DIRECTION OF CURRENT IN LOOP EQUATIONS In complex circuits, you often will NOT know the DIRECTION OF CURRENTS, so you will _________ / _________ them:

(0) NEW: ____________ direction of ALL currents

(1) LABEL +/– Signs Battery + is on longer terminal. Resistor + is where ___________ enters the resistor. (2) “CROSS” elements in chosen DIRECTION OF LOOP, adding the voltage if you crossed from _____ to _____.

EXAMPLE: Write Loop Equations for the circuits below, based on the indicated direction of current, then find their current. (a) current is clockwise (b) current is counter-clockwise

2Ω 4V

1Ω 10V

2Ω 4V

1Ω 10V


CH 19: DC CIRCUITS

CONCEPT: SOLVING CIRCUITS WITH MULTIPLE SOURCES

We combine Kirchhoff’s Junction Rule (𝚺 I IN = 𝚺 I OUT) and Loop Rule (𝚺 V = 0) to solve circuits with MULTIPLE sources:

1) LABEL DIRECTIONS:

LABEL Junctions, Loops (arbitrary) and direction of Currents (assumed)

LABEL +/- on Voltage Sources (+ terminal) and Resistors (current enters) 2) WRITE EQUATIONS:

WRITE a Junction Equation for each Junction

WRITE a Loop Equation for each Loop 3) SOLVE SYSTEM OF EQUATIONS

EXAMPLE: For the circuit below, find the current through each of the 3 branches.

10Ω 15Ω 9V

5V


CH 19: DC CIRCUITS

PRACTICE: FIND ALL CURRENTS USING KIRCHHOFF’S RULES For the circuit below, find the current through each of the 3 branches.

1Ω

2V

3Ω

4V

5Ω


CH 19: DC CIRCUITS

CONCEPT: COMBINING VOLTAGE SOURCES IN SERIES You can combine Voltage Sources connected in SERIES to simplify the circuit VEQ = ______________ - If the Voltage Sources are pushing charge in OPPOSITE directions, their voltages will ________________. EXAMPLE: For each circuit below, combine the batteries and resistors, then find the magnitude and direction of the current.

(a) (b)

2Ω 5V

3Ω 10V

2Ω 5V

3Ω 10V


CH 19: DC CIRCUITS

EXAMPLE: FIND TWO VOLTAGES IN 2-BATTERY CIRCUIT For the circuit below, calculate voltages V1 and V2.

8Ω 18V

4Ω V1

6Ω V2

5A

4A


CH 19: DC CIRCUITS

PRACTICE: FIND ONE VOLTAGE AND ONE CURRENT IN 2-BATTERY CIRCUIT For the circuit below, calculate (a) the voltage V1 shown, and (b) the current through the 6-Ohm resistor.

6Ω 12V

4Ω 4A

V1 3Ω


CH 19: DC CIRCUITS

PRACTICE: FIND VOLTAGE OF ONE RESISTOR IN 2-BATTERY CIRCUIT

For the circuit below, calculate the voltage across the 100-Ohm resistor.

20Ω 100Ω

40V

80Ω

60V


CH 19: DC CIRCUITS

CONCEPT: HOW TO CHECK YOUR WORK (KIRCHHOFF’S RULES)

Once you know ALL values (voltages, currents, and resistances) in a circuit, you can check your with a simple rule:

- ALL branches MUST have the same magnitude and “direction” (_________________) of __________________.

EXAMPLE 1: Check if all numbers below “match up”

EXAMPLE 2: Check if all numbers below “match up”

8Ω, 5A 18V

4Ω, 9A 58V

6Ω, 4A 2V

6Ω, 0.67A 12V

4Ω, 4V

30V 4,67A, 3Ω


CH 19: DC CIRCUITS

CONCEPT: COMBINING CAPACITORS IN SERIES AND PARALLEL

In Circuit problems, we can COLLAPSE / COMBINE capacitors into a SINGLE ___________________ capacitor.


- Direct connection, - Equivalent Capacitance:

𝟏

𝐂𝐞𝐪= __________________

- Splits off, forms a loop - Equivalent Capacitance:

𝐂𝐞𝐪 = _________________

For circuits with combinations, find Ceq’s from inside → outside. EXAMPLE: What is the equivalent capacitance of the following capacitors?

For TWO capacitors in SERIES, 𝐶𝑒𝑞 = ________

EXAMPLE: What is the equivalent capacitance of the following capacitors?

1 F 3 F

4 F 2 F

2 F

2 F

1 F

4 F


CH 19: DC CIRCUITS

EXAMPLE: EQUIVALENT CAPACITANCE OF 4 CAPACITORS

What is the equivalent capacitance of the following combination of capacitors?

PRACTICE: EQUIVALENT CAPACITANCE OF 4 CAPACITORS

What is the equivalent capacitance of the following capacitors?

2 F 2 F

3 F

5 F

2 F

2 F

3 F 2 F


CH 19: DC CIRCUITS

CONCEPT: SOLVING CAPACITOR CIRCUITS

In Circuit problems, you’ll be asked to find CHARGE and VOLTAGE across combinations of capacitors.


- Equivalent Capacitance:

𝟏/𝐂𝐞𝐪 = 𝟏/𝐂𝟏 + 𝟏/𝐂𝟐 + 𝟏/𝐂𝟑

- Share [ CHARGE | VOLTAGE ] with EACH OTHER

- Share [ CHARGE | VOLTAGE ] with Ceq

- Equivalent Capacitance:

𝐂𝐞𝐪 = 𝐂𝟏 + 𝐂𝟐 + 𝐂𝟑

- Share [ CHARGE | VOLTAGE ] with EACH OTHER

- Share [ CHARGE | VOLTAGE ] with Ceq

STEPS FOR CAPACITOR CIRCUITS

1) Find SINGLE EQUIVALENT capacitor

2) Find V & Q for Ceq

3) Work backwards to find V & Q for each capacitor

EXAMPLE: What is the charge and voltage of each of the capacitors in the following circuit?

2 F

1 F

6 F

10 V


CH 19: DC CIRCUITS

PRACTICE: FIND CHARGE & VOLTAGE IN ALL CAPACITORS

What is charge and voltage across each capacitor below?

EXAMPLE: FIND CHARGE OF ONE CAPACITOR

What is the charge on the 3 F capacitor below?

2 F 2 F

3 F

10 V

5 V

1 F

3 F

4 F 2 F


CH 19: DC CIRCUITS

PRACTICE: FIND VOLTAGE OF THE BATTERY

What is the voltage of the battery below?

PRACTICE: FIND CHARGE OF CAPACITOR IN A COMPLEX ARRANGEMENT

What is the charge on the 5 F capacitor?

1 F

V = ?

3 F

1 F

2 F

3 C


CH 19: DC CIRCUITS

physics - giancoli 7e ch 19: dc...

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