Solving multiple equations through an array

I am trying to solve multiple equations in an array but am getting too many answers for one equation.

>> P = sym('P', [1 3]);
>> V = sym('V', [1 3]);
>> R_ON = [1 2 3];
>> P = ((200-V)./100).*V==(V.^2)./R_ON
P =
 
[ -V1*(V1/100 - 2) == V1^2, -V2*(V2/100 - 2) == V2^2/2, -V3*(V3/100 - 2) == V3^2/3]

>> solve(P).V1
 
ans =
 
       0
       0
 200/101
 200/101
       0
       0
 200/101
 200/101

Why is the solution giving me repeated values and 8 solutions? There should only be the two solutions, 0 and 200/101. Thanks in advance!

Answer 1

[Star Strider]

Displaay at all the solutions to understand what solve is doing —

P = sym('P', [1 3]);
V = sym('V', [1 3]);
R_ON = [1 2 3];
P = ((200-V)./100).*V==(V.^2)./R_ON

P = 

% P =
% [ -V1*(V1/100 - 2) == V1^2, -V2*(V2/100 - 2) == V2^2/2, -V3*(V3/100 - 2) == V3^2/3]
S = solve(P)

S = struct with fields:
    V1: [8×1 sym]
    V2: [8×1 sym]
    V3: [8×1 sym]

S.V1

ans = 

S.V2

ans = 

S.V3

ans = 

.

[Josh Frisby]

Okay, so it is really combinding all 3 equations into one and trying to solve? How do I get it to solve each equation independently? Like solve: -V1*(V1/100 - 2) == V1^2 for V1 then solve -V2*(V2/100 - 2) == V2^2/2 for V2 and finally solve -V3*(V3/100 - 2) == V3^2/3 for V3?

[Star Strider]

It is not possible to solve for them independently, since ‘V’ and ‘P’ are vectors.

Solve for ‘V’ then choose the element of the solution that you want.

.

[Josh Frisby]

Well your answer and comment put me on the right path at least. The code below fully encapsulates what I was trying to achieve. I encorporated a for loop to solve for each equation independly of each other. Thanks.

sympref('FloatingPointOutput',true); %store values in symbol type as floats
V_DS = sym('V_DS', [1 41]); %define V_DS as array of symbols
V = sym('V', [1 41]); %define V as array of symbols
P = sym('P', [1 41]); %define P as array of symbols
T=linspace(0,200,41); %define temps in range from 0-200 increasing by increments of 5
R_ON = 0.0133.*T+1.667; %create an array of R_ON values for each temp
assume(V>0); %only store solutions greater than 0 for V
V = ((200-V)./100).*V==(V.^2)./R_ON; %create an array of voltage equations for each R_ON value
for i = 1:41
    V_DS(i) = solve(V(i)); %solve and store each voltage equation for V
    P(i) = (V_DS(i).^2)./R_ON(i); %solve for power associated with each voltage
end
%create table
Table = table(T',R_ON',double(V_DS'),double(P'), 'VariableNames', {['Temp(' char(176) 'C)'],'R_ON(Ω)','V_DS(V)','P(W)'})
%create plot with settings
figure
hold on;
plot(T,double(P),'Color','b','Marker','+','MarkerFaceColor','#A2142F','MarkerEdgeColor','#A2142F');
xlabel("Temperature (" + char(176) + "C)",'FontSize',14,'Color','#7E2F8E');
ylabel("Power (W)",'FontSize',14,'Color','#7E2F8E');
title("Power (W) VS Temperature (" + char(176) + "C)",'Color','#7E2F8E');
set(gca,'FontSize',20,'XColor','#7E2F8E','YColor','#7E2F8E');

[Star Strider]

As always, my pleasure!