1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zloy xaker [14]
2 years ago
12

Calculate the equivalent resistance Req of the network shown in Fig. 3.87 if R1 = 2R2 = 3R3 = 4R4 etc. and R11 = 3

Mathematics
1 answer:
son4ous [18]2 years ago
7 0

The equivalent resistance of the network shown is: R_{eq}=16.463\Ohm

So, first of all, we can start by determining what each of the resistances is equal to. In this case we can start by saying that R_{1}=11R_{11} This means that:

R_{1}=11(3\Ohm)

Therefore:

R_{1}=33\Ohm

We can now use this value to find the value of the other resistances. The given condition for the resistances can be represented with the following formula:

R_{n}=\frac{R_{1}}{n}

so:

R_{2}=\frac{R_{1}}{2}=\frac{33}{2}\Ohm

R_{3}=\frac{R_{1}}{3}=\frac{33}{3}\Ohm=11 \Ohm

R_{4}=\frac{R_{1}}{4}=\frac{33}{4}\Ohm

R_{5}=\frac{R_{1}}{5}=\frac{33}{5}\Ohm

R_{6}=\frac{R_{1}}{6}=\frac{33}{6}\Ohm=\frac{11}{2}\Ohm

R_{7}=\frac{R_{1}}{7}=\frac{33}{7}\Ohm

R_{8}=\frac{R_{1}}{8}=\frac{33}{8}\Ohm

R_{9}=\frac{R_{1}}{9}=\frac{33}{9}\Ohm=\frac{11}{3}\Ohm

R_{10}=\frac{R_{1}}{10}=\frac{33}{10}\Ohm

R_{11}=3\Ohm

So now that we know what each resistance is equal to, we can go ahead and analyze the circuit.

In this case we can see that R_{10} and R_{11} are parallel, so we can calculate their equivalent resistance.

R_{1011}=\frac{R_{10}R_{11}}{R_{10}+R_{11}}

Which yields:

R_{1011}=\frac{(\frac{33}{10}\Ohm)(3\Ohm)}{\frac{33}{10}\Ohm+3\Ohm}

R_{1011}=\frac{11}{7}\Ohm

Now, R_{8}, R_{9} and R_{1011} are connected in series, so we can calculate their equivalent resistance like this:

R_{891011}=R_{8}+R_{9}+R_{1011}

R_{891011}=\frac{33}{8}+\frac{11}{3}+\frac{11}{7}

R_{891011}=\frac{1573}{168}\Ohm

Now,  we can see that R_{7} and R_{891011} are parallel, so we can calculate their equivalent resistance.

R_{7891011}=\frac{R_{7}R_{891011}}{R_{7}+R_{891011}}

Which yields:

R_{7891011}=\frac{(\frac{33}{7}\Ohm)(\frac{1573}{168})}{\frac{33}{7}\Ohm+\frac{1573}{168}\Ohm}

R_{7891011}=\frac{4719}{1505}\Ohm

Now, R_{5}, R_{6} and R_{7891011} are connected in series, so we can calculate their equivalent resistance like this:

R_{567891011}=R_{5}+R_{6}+R_{7891011}

R_{567891011}=\frac{33}{5}\Ohm+\frac{11}{2}\Ohm+\frac{4719}{1505}\Ohm

R_{567891011}=15.236\Ohm

Next,  we can see that R_{4} and R_{567891011} are parallel, so we can calculate their equivalent resistance.

R_{4567891011}=\frac{R_{4}R_{567891011}}{R_{4}+R_{567891011}}

Which yields:

R_{4567891011}=\frac{(\frac{33}{4}\Ohm)(15.236\Ohm)}{\frac{33}{4}\Ohm+15.236\Ohm}

R_{4567891011}=5.352\Ohm

Now, R_{2}, R_{3} and R_{4567891011} are connected in series, so we can calculate their equivalent resistance like this:

R_{234567891011}=R_{2}+R_{3}+R_{4567891011}

R_{234567891011}=\frac{33}{2}\Ohm+11\Ohm+5.352\Ohm

R_{234567891011}=32.852\Ohm

Finally, we can see that R_{1} and R_{234567891011} are parallel, so we can calculate their equivalent resistance.

R_{eq}=\frac{R_{1}R_{234567891011}}{R_{1}+R_{234567891011}}

Which yields:

R_{eq}=\frac{(33\Ohm)(32.852\Ohm)}{33\Ohm+32.852\Ohm}

R_{eq}=16.463\Ohm

See attached picture for images on how to reduce the circuit.

You can find further information in the following link.

brainly.com/question/21538325?referrer=searchResults

You might be interested in
Factorise x squared + 4x + 3 ​
olganol [36]
<h3>Answer:  (x+1)(x+3)</h3>

===================================================

Explanation:

Let's assume it factors into (x+a)(x+b)

The goal is to find the two numbers a and b.

FOIL out (x+a)(x+b) to get x^2+(a+b)x+ab

Note how a+b is the middle term and ab is the last term.

In the original expression, 4 is the middle term and 3 is the last term.

So we need to find two numbers that

  • add to 4
  • multiply to 3

There are two ways to multiply to 3 and they are

  • 1 times 3 = 3
  • -1 times -3 = -3

But only the first way has the factors add to 4. So that means a = 1 and b = 3.

Therefore (x+a)(x+b) = (x+1)(x+3)

And x^2+4x+3 = (x+1)(x+3)

8 0
3 years ago
7,243 ÷ 4.<br><br> What is the remainder?
Sveta_85 [38]
Divested using long division
1810 r 3
4 0
3 years ago
State whether the following number is divisible by 2,5, or 10. 215
adoni [48]

Answer

215 can only be divided by 5

4 0
2 years ago
Simplify this expression: (a^8*a^6)^1/7/a^2
Ulleksa [173]
<span><span>Simpliest form is a^2/a^2 to get 1

</span></span>

3 0
2 years ago
I only need to know question b, if anyone can help
kicyunya [14]

243 liters represents 7/10 - 1/4 of the water.

v=243 / (7/10 - 1/4) = 243 / (14/20-5/20) = 243(20)/9 = 540 liters.

Answer: 540 liters

Check:

(7/10)(540) = 7(54) = 378

(1/4)540 = 135

difference = 378 - 135 = 243  good

5 0
3 years ago
Other questions:
  • Two angle measures in a scalene triangle are 77° and 62°. what is the measure of the third angle
    13·1 answer
  • If a race car averages 155 miles per hour for 4 hours, how far does the car travel?
    8·2 answers
  • A chess player moves a knight from the location (3, 2) to (5, 1) on a chessboard. If the bottom-left square is labeled (1, 1), t
    10·2 answers
  • Domain and range of f(x)=sqrt(x^2 -4)
    10·1 answer
  • A fruit company sells oranges for 32 cents a pound plus $7.50 per order for shipping. If an order is over 100 pounds, shipping c
    6·1 answer
  • I NEED HELP WITH THIS
    15·2 answers
  • In the diagram below, AB is parallel to CD. What is the value of x?
    5·1 answer
  • Please any math experts help thanks you
    14·1 answer
  • Prove that (vectors)
    6·1 answer
  • 4y divided by 3 Can someone tell me how to write this out and get my answer? Thank you
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!