Mathematics, 11.08.2021 14:00 hernandezbrandon059

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

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

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Answer from: mxdv

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.

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

Answer from: Quest

25% is the answer

Answer from: Quest

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: