Question: Resistors connected in parallel/ series

In summary, the equivalent resistance of several resistors connected in parallel is always lower than the smallest valued resistor. The two circuits shown in the image are not equivalent, as the circuit on the left has a resistor while the circuit on the right does not. For three resistors connected in series, the voltage across each resistor is not always equal, as it depends on the individual resistance values.
  • #1
cathode
11
0

Homework Statement



1.The equivalent resistance of several resistors connected in parallel is always lower than the smallest valued resistor.

A) True
B) False


2. The following two circuits are equivalent at terminals A-B.

http://img6.imageshack.us/img6/1401/circuity.jpg [Broken]

A) True
B) False


3. For three resistors connected in series, the voltage across each resistor is equal even if the resistors have different values.

A) True
B) False

----

For number 1, I guessed True. I'm not sure but my reasoning behind is by KCL and KVL, voltages around a loop and current entering a node is zero at every instant. Again, I'm not sure about this one.

For number 2, I guessed False. The cicuit on the left, I used Ohm's law to find its voltage; 50(v). On the other hand, the right circuit doesn't have a resistor at all. So I thought since 50(v) is greater than 0 (v) {the right circuit}, the statement is false, which states two circuits are equivalent.

For number 3, I guessed True, because by the definition KVL, the sum of voltages around a loop equals zero.

I'm confident about my answer for number 3, but I'm doubtful about 1 and 2.
 
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  • #2
Note: I'm commenting about your reasoning but not saying any of your answers are wrong...or right. It's not sufficient to guess correctly but to know why which I assume you already appreciate.


Number 1 start with the smallest valued resistor by itself. If you add another in parallel will the total resistance go up or down?

Number 2 your reasoning looks good.

In number 3 there is no mention of a loop. You have three resistors in series. That means current flowing through anyone flows through them all so the currents are equal. How does this relate to the voltages?
 
  • #3
For 1, the total resistance will go up.

For 2, I checked my textbook, and there is an example that shows a circuit and a equivalent circuit of its original circuit. Turns out, I was wrong. This one is actually True.

For 3, that means the total voltage passing through each resistor is equal to the total resistance of the three resistors.

R1 ---- R2 ---- R3
3ohms 4ohms 5ohms
3volts 4volts 5volts


Therefore, it's false!
 
  • #4
cathode said:
For 1, the total resistance will go up.
Think of a stream analogue. If you dig a channel parallel to the stream do you get more or less flow? (more flow = less resistance, less flow = more resistance)?
For 2, I checked my textbook, and there is an example that shows a circuit and a equivalent circuit of its original circuit. Turns out, I was wrong. This one is actually True.
I thought the question vague. Was there more detail about the meters?
For 3, that means the total voltage passing through each resistor is equal to the total resistance of the three resistors.

R1 ---- R2 ---- R3
3ohms 4ohms 5ohms
3volts 4volts 5volts


Therefore, it's false!
Right!

Nothing beats a nice concrete example to clarify!
 
  • #5
About question number 2. You have an ideal current source. The current in terminal A will be 5A, whether there is a resistor in series or not.
 
  • #6
CEL said:
About question number 2. You have an ideal current source. The current in terminal A will be 5A, whether there is a resistor in series or not.

Ahhh! I didn't recognize that particular circuit element. That explains it. Does that make sense to you Cathode?
 
  • #7
cathode said:

Homework Statement



1.The equivalent resistance of several resistors connected in parallel is always lower than the smallest valued resistor.

A) True
B) False

Why don't you just try a few with a calculator? For example, the parallel combination of 10 ohms and 90 ohms would be 9 ohms. What general pattern emerges from such results?
 
  • #8
Hi Cathode,
for question

3. For three resistors connected in series, the voltage across each resistor is equal even if the resistors have different values.

A) True
B) False

>>> The answer should be B) False. Different resistor value gives different voltage as the current is the same in series.
 
  • #9
I'm still not understanding about question 1...
 
  • #10
cathode said:
I'm still not understanding about question 1...

For simplicity, consider two resistors: R1 and R2. What is the resistance of their parallel connection?
 
  • #11
is the relationship, the product over sum rule?
 
  • #12
cathode said:
is the relationship, the product over sum rule?

Yes, if the number of resistors in parallel is exactly two.

If there are two, then the more general expression R = 1/[(1/R1)+(1/R2)] will also be equal to R1 R1 / R1 + R2. But don't try using the product over the sum if there are three or more resistors.
 
  • #13
cathode said:
is the relationship, the product over sum rule?

Yes.
[tex]R_{eq}=\frac{R_1R_2}{R_1+R_2}[/tex]
Suppose [tex]R_2[/tex] is the smaller resistor. Divide the numerator and the denominator by [tex]R_1[/tex]. You get:

[tex]R_{eq}=\frac{R_2}{1 + R_2/R_1}[/tex].
Since [tex]R_2[/tex] is divided by a quantity greater than 1, the result must be smaller than [tex]R_2[/tex].
You can consider the parallel of three resistors as the parallel of one with the equivalent of the parallel of the other two and so on.
 
  • #14
ahh now I get it.
Thanks so much for the help, everyeon!
 

1. What is the difference between resistors connected in parallel and series?

Resistors connected in parallel have the same voltage across each resistor, while resistors connected in series have the same current passing through each resistor. Additionally, the equivalent resistance for resistors in parallel is less than the individual resistances, while the equivalent resistance for resistors in series is the sum of the individual resistances.

2. How do you calculate the equivalent resistance for resistors in parallel/ series?

For resistors in parallel, the equivalent resistance is calculated using the formula 1/Req = 1/R1 + 1/R2 + ... + 1/Rn. For resistors in series, the equivalent resistance is simply the sum of the individual resistances.

3. What happens to the total resistance when resistors are connected in parallel/ series?

The total resistance decreases when resistors are connected in parallel, as the equivalent resistance is less than the individual resistances. Conversely, the total resistance increases when resistors are connected in series, as the equivalent resistance is the sum of the individual resistances.

4. Why is it important to understand how resistors are connected in parallel/ series?

Understanding how resistors are connected in parallel/ series is important in circuit design and analysis. It allows us to calculate the total resistance in a circuit and determine the current and voltage at different points in the circuit.

5. How does the power dissipation differ between resistors connected in parallel and series?

For resistors in parallel, the power dissipated by each resistor is less than the total power supplied to the circuit. For resistors in series, the power dissipated by each resistor is equal to the total power supplied to the circuit. This is because the power dissipated by a resistor is proportional to the current passing through it, and in parallel circuits, the current is split between multiple resistors.

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