cahier physique - physics workbook

Series Circuit - effective resistance

lab series resistance

1) read and fill blanks: When resistors are connected in series, all current travels through each resistor, one after the other. It is pretty much like water falling from a height and operating several small wheels. The same quantity of water flow through each wheel. In the circuit below all ammeter read the same ____________.

There is a voltage drop for each resistance. V = V1 + ____ + _____. V1 is the voltage drop for R1, V2 is the voltage drop for _____ and V3 is the voltage drop for _______. V1 = R1 I and V2=_______ and V3 = ______ for each resistance. Let's do some Math.
If V = V1 + V2 + V3 show that V = Reff I with Reff = R1 + R2 + R3
Reff is called the effective resistance.
It is the resistor that could replace all resistors in the circuit.
Every thing happens like the circuit is replaced by:

With V = Reff I. All the ammeters have the same reading for I.
The effective resistance , Reff, of resistors in series is the sum of the resistances. THe current through a series circuit is found by calculating the effective resistance R, and then using Ohm's law in the form I = V/Reff/ We will see other examples.

2) Observe the diagram below. THe current is everywhere 1A. The voltage of the battery 12V will drop each time the current will go trough a resistance..

A) V1 = _________. The current goes through R1 so the voltage drops by _____ V. Energy has been used by ____ J /C. use Ohm's law
B) V2 = ________. The current passed R1 and R2 so the voltage has dropped _______V.
C) V3 = ___________. The current is back to the battery after passing through R1, R2, R3 .
The voltage dropped a total amount of _______.
D) Find the effective resistance R eff = ________.
E) Draw a new circuit in series that includes the battery (12V) and the effective resistance Reff.
(use the right symbols)

F) Using Ohm's law find the current in the circuit. I = ______ A.
G) what is the potential drop after the current go through the unique resistance ________.
H) conclusion: If you have a circuit in series, just replace the resistances by the Reff = ___________________.

3) Four 15 Ω resistors are connected in series to a 30V battery.
What is the current in the circuit? Draw the circuit .
(find Reff, use Ohm's law)

4) Three 20 Ω resistors are connected in series across a 120V generator.
A) what is the effective resistance of the circuit ?
B) What is the current in the circuit ?

5) a 10 Ω resistor, a 15Ω resistor and a 5 Ω resistor are connected in series across a 90V battery.
A) What is the effective resistance of the circuit ?
B) What is the current in the circuit ?

6) Ten Christmas tree bulbs connected in series have equal resistances. When connected to a 120V outlet, the current through the bulbs is 0.6A.
A) What is the effective resistance of the circuit ?(use Ohm's law)
B) what is the resistance of each bulb ?

7) A lamp having a resistance of 10 Ω is connected across a 15V battery.
A) What is the current through the lamp ?
B) WHat resistance must be connected is series with the lamp to reduce the current to 0.5A ?

8) A 5 Ω resistor and a 100 Ω resistors are connected in series and placed across a 45V potential difference.
A) What is the effective resistance of the circuit ?
B) what is the current through the circuit ?
C) What is the voltage drop across each resistor ?
D) What is the total voltage drop across the circuit ?

9) an important application of series resistors is the voltage divider. THe voltage divider is designed to obtain a desired voltage from a battery that supplies a larger voltage. Consider the circuit below.

don't use any number. Use Algebra.
A) Find I in term of V, R1 and R2. I = _____________
B) The voltage V2 = R2 I = __________. (substitute I by the expression found in A)
C) So you can chose the right value of R1 and R2 such as you get the voltage V2 you need.
(V2 is smaller than V). It is like having a new battery. So why is it called a voltage divider?

10) Use the expression of V2 found in A.
A 9V battery and two resistors, R1= 400Ω and R2 = 500Ω are connected as a voltage divider. What is the voltage across R2 ?

11) In a voltage divider with V = 9V, R1=500Ω and R2 is a photoresistor.
A) What is the output voltage, V2 across R2, when a bright light strikes the photocell and
R2 = 4.0 10² Ω
B) When the light is dim, R2 = 4.0 10³ Ω. WHat is V2 ?
C) When the photoresistor is in the dark , R2= 4 105 Ω. What is V2 ?

12) REview
Three resistors of 3 Ω, 5 Ω and 4 Ω are connected in series across a 12V.
A) What is the effective resistance of the 3 resistors ?
B) What is the current in the circuit ?
C) What is the voltage drop across each resistor ?
D) What is the total voltage drop across the circuit ?

PARALLEL CIRCUIT
lab parallel circuit

1) Please observe and read

Using a battery (1.5 V) and 3 bulbs (R1 = R2 = R3= 10Ω) try to build the circuit above. Build 3 bulbs (3 resistances) in parallel. Using a voltmeter find the voltage drop across each bulb.
You should find that the voltage is ____________. V1 = V2 = V3 = _______. Observe the model using a water pump. The potential energy is the same for the 3 outputs. The water coming out of each pipe could be used to supply the same energy to different devices. (generator ? mechanical system like pulley ? wheel ? ...). In the above example, the size of each pipe is the same. So the amount of water coming out of each branch (pipe)is __________ . In our circuit since the bulbs are the same, their need in energy is the same (same 10 Ω resistance) , so the current flowing through each branch is the ___________.

Suppose I is the current produced by the battery, I1 is the current flowing through the 1st bulb (1st branch), I2 is the current flowing through the second bulb (2nd branc) , I3 is the current flowing through the third bulb (third branch).
In a parallel circuit: I = I1 + I2 + I3
(The total amount of water from the pump = sum of water flowing in each pipe)
The total current in a parallel circuit is the sum of the currents in its branches.

Let's try to I1, I2, I3 and then I. We have V = 1.5V and R1 = R2= R3 = 10 Ω

According to Ohm's law: V = R I. Use this relationship (V1= R I1) to find I1 = _____

I2 = _____ I3 = ________. So I = _______.

There is another way to find I. We could replace the 3 branches by only one with a unique resstance Reff or Requivalent.

For a parallel circuit the effective resistance is given by the question:
1/ Reff = 1/R1 + 1/R2 + 1/R3
you need then to solve for Reff, given R1= R2 = R3 = 10Ω

Reff = _______. Use V = Reff I to find I. (V=1.5V). I = _______

Do you find the same value for I? Compare Reff to R1 or R2 or R3 : Reff _____ any resistance.
In a serie circuit, it is the opposite. Reff ____ R1 or R2 or ...

2)

3 resistors are connected in parallel across a 12V difference in potential
A) Find the effective resistance Reff
(use 1/Reff = 1/R1+1/R2+1/R3)
B) Replace the 3 branches circuit by a simple circuit with only one resistor. Draw the circuit. What is the resistance ?

C) Using this new circuit find the current I in the entire circuit. Reff= ______ (use V = Reff I)
D) Using the 3 branches circuit, find the current through each branch of the circuit.
I1 = ___ I2 = _____ I3 = ________
E) Find I1 + I2 + I3 =_____. conclusion ?
F) Compare Reff to R1, R2, R3 ?

3)

In a parallel circuit what happens if one of the bulb die ?
If you connect the bulb in series instead, what happens if one of the bulb die ?
Why do you think your appliances in your home are connected in parllel ? see image below.

4) The 2 kinds of connections are shown below

For each of this question, write the form that applies: series circuit or parallel circuit.
A) the current is the same throughout
B) The total resistance is equal to the sum of the individual resistances.
C) The voltage drop is the same across each resistor.
D) The voltage drop is proportional to the resistance.
E) Adding a resistor in the circuit decreases the total resistance.
F) Adding a resistor in the circuit increases the total resistance.
G) If one resistor is turned off or broken, there is no current in the entire circuit.
H) If one resistor is turned off, the current through all other resistors remains the same.
I) suitable for house wiring.

5) extra credits to hand on a separtate sheet of paper. Explain the function of a fuse in an electric circuit. (do some research on your own). What is the short circuit ? What could happen then and how it happens?

6) Three 15 Ω resistors are connected in parallel and placed across a difference in potential of 30V.
A) What is the effective resistance of te parallel circuit ?

B) What is the current through the entire circuit?

C) What is the current through each branc of the circuit ?

7) A 120 Ω resistor, a 60 Ω resistor, and a 40 Ω resistor are connected in parallel and placed across a potential difference of 120V.
A) What is the effective resistance of the parallel circuit ?

B) What is the current in the entire circuit ?

C) What is the current through each branch of the circuit ?

8) A 6Ω resistor, an 18Ω resistor, and a 90 Ω resistor are connected in parallel and placed across a 36V potential difference.
A) What is the current through each resistor ? (V = RI)

B) What is the total current in the circuit ? ( I = I1 + I2 + I3)

C) What is the effective resistance of the circuit ? ( 1/Reff = 1/R1 + 1/R2 + 1/R3)

9) A 75 Ω heater and a 150Ω lamp are connected in parallel across a potential difference of 150V.
A. What is the current through the 75 Ω heater ?

B) What is the current through the 150 Ω lamp ?

C) What is the current through the entire circuit ?

D) What is the effective resistance of the entire circuit ?

E) Divide the voltage by the effective resistance. Does the result agree with the solution to Part C).

10)

This is a more complex circuit. It is composed paralell resistors (R1= 6 and R2 = 12) in serie with the R3 = 8 Ω. We need to replace the circuit by a simpler one with only effective resistor Rtot. Let's find Rtot.
A) The 2 resistors (6 and 12) can be replaced by one unique resistor Reff. Find Reff and draw the new circuit.
(1/Reff = 1/R1 + 1/R2 )

B) You have now a new circuit with 2 resistors (R3 and Reff1) connected in series.
Find Rtot. Draw the new circuit. (of course Rtot = Sum of all resistors)

C) Find the total current I through Rtot produced by the battery(use Rtot and V =1.5V and Ohm's law)

D) Find the voltage across the 8 Ω resistor. (use Ohm's law V = R3 I)

E) Using the D) answer, can you find the voltage drop across the resistors R1 and R2 (6 and 12).
Of course they both have the same voltage. (total voltage drop =1.5V = drop across R1 + drop across the // circuit)

F) Can you find the current in each branch of the parallel circuit ? I1 and I2? Use the answer from E) and Ohm's law. (V found in E = R1 I1 , solve for I1 and V found in E = R2 I2 , solve for I2)

11)

THis is a project for you to work on. Please team up. I will grade the work.
You need to find:
A)Reff1 the effective resistance for the 1st // circuit (with R1, R2) and Reff2 the effective resistance for the // circuit (with R3, R4)
B) Rtot the effective resistor for the whole circuit.

C) the total current I produced by the battery .

D) using A), the voltage across R1, R2, R3, R4 (of course R1 and R2 have the same voltage and so do R3 and R4)

E) the currents I1 (across R1), I2, I3, I4