Having some difficulty with this; not sure to what extent help can be given with

Question

Having some difficulty with this; not sure to what extent help can be given with Excel problems, but here it is!

What value of k will result in V4 = 20V? To hold V4 to a tolerance of (20±0.1)V, what range of integers should k be held to? Given the tolerance for k you just calculated, how will V1, V2, and V3 vary?

To answer these questions, you should set up another Excel worksheet. Nodal analysis at V4 yields an equation relating V3 and V4. Since there are three values of V4 to consider, it is inconvenient to use your calculator. Instead, you will use Excel to calculate the complete set of values by setting up columns appropriately. For each desired value of V4, Excel will compute the corresponding value of V3. Then, nodal analysis at V3 yields an equation relating V2, V3, and V4. Since you know V3 and V4, you can now solve for V2, and so on, until you can calculate the desired value of k. In particular, your formula for k should depend on the cell identifiers for the four node voltages.

Once you have calculated V3, V2, V1, and k for V4 = 20V, copy the formulas into adjoining columns to calculate them for V4 = 20.1V and 19.9V.

Here is a new way to copy cells: Highlight all three columns (i.e., not the column of labels), with the desired formulas in the left-most column, then “fill right” using a pull-down menu (Edit > Fill > Right) or keystroke (CTRL-R on both Macs and PCs).

Here is an even faster way to copy cells: Highlight the first column of values (for V4 = 20V), as before. Hover over the lower right corner of the bottom-most cell (do not click, just hover; if you click, you will see the highlighting disappear). While hovering, you should see the cursor change. (On a PC, it changes to a thin, black cross.) Now click and drag to the right, releasing the mouse only when you have highlighted the other two columns. Your formulas have been copied!

Once the formulas are copied, change the values of V4 to 20.1 and 19.9 in the new columns, and you will see all the other values change.

Note that you do not need to have separate cells for each component of the circuit (as you did for problem P5). Instead, derive your relationships and simplify them as much as possible before entering them into Excel as formulas. Your spreadsheet should be 4 columns by 5 rows, where the first column is used to label the rows, and the five rows show the values of the four node voltages and k. You can add a header row if you want to label the columns.

Explanation / Answer

First of all, i don't think u need an excel spread sheet for this problem. This problem is just having simple calculations that u can do using a calculator. Here is the answer.....

Nodal Analysis

Desired V4 = 20 V

Allowed tolerance = ±0.1 v

So, we have three values of V4

V4= 20 v

V4= 20.1 v

V4= 19.9 v

Writing KCL at V4

[V4/ 20] - [1.5] + [(V4-V3)/ 20] = 0

=> 2V4 - V3 = 30 ----(1)

for different desired values of V4, calculate V3 using eq (1) and update table

V4= 20 V       V3= 10 V

V4= 20.1 V     V3= 10.2 V

V4= 19.9 V     V3= 9.8 V

Writing KCL at V3

[(V3-V4)/ 20] - [2Vx] + [(V3-V2)/ 10] = 0 ----- (2)

Vx is the voltage drop across 5 resistor, from the circuit, we can write Vx = I5 x 5

I5 = (V2- 7.2)/ 10 => Vx = (V2- 7.2)/ 2 ---- (3)

Substitute (3) in (2)

we get, 22V2- 3V3 + V4 = 0 ----- (4)

Substitute different values of V4, V3 to find out corresponding values of V2 and update the table

V4= 20 V       V3= 10 V       V2= 7 V

V4= 20.1 V     V3= 10.2 V    V2= 7.02 V

V4= 19.9 V     V3= 9.8 V     V2= 6.98 V

Writing KCL at V2

[(V2- V1)/ 20] + [(V2- 7.2)/ 10] + [(V2- V3)/ 10] = 0

=> -V1 + 5V2 - 2V3 = 14.4 ----- (5)

Substitute different values of V3 & V2 to find out corresponding values of V1 and update the table

V4= 20 V       V3= 10 V       V2= 7 V        V1= 0.6 V

V4= 20.1 V     V3= 10.2 V    V2= 7.02 V    V1= 0.3 V

V4= 19.9 V     V3= 9.8 V     V2= 6.98 V     V1= 0.9 V

Writing KCL at V1

[V1/ 20] + [(V1- kVx)/ 10] + [(V1- V2)/ 20] = 0

=> 4V1 - (1+k) V2 + 7.2 k = 0 ------ (6)

Substitute different values of V1 & V2 to find out corresponding values of k and update the table

V4= 20 V       V3= 10 V       V2= 7 V        V1= 0.6 V     k= 0.324

V4= 20.1 V     V3= 10.2 V    V2= 7.02 V    V1= 0.3 V    k= 0.409

V4= 19.9 V     V3= 9.8 V     V2= 6.98 V     V1= 0.9 V    k= 0.238       Ans

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