Newton Raphson Method to solve the non linear circuits

The Newton-Raphson method consists in  obtain improved values of the approximate
root through the recurrent application of equation above. For example, the second third approx to that root will be given by
x2 = x1 - f(x1)/f'(x1),
and
x3= x2 - f(x2)/f'(x2),
respectively.
This iterative procedure can be generalized by writing the following equation, where i
represents the iteration number:
xi+1 = xi - f(xi)/f'(xi).
After each iteration the program should check to see if the convergence condition,
namely,
|f(x i+1)|<ε,
is satisfied.This was actually a brief explanation of how newton raphson method works.Now let's have a example on  newton raphson method . 

Consider a circuit whose current  & resistors are known and we have to find the value of voltage.In this case.

CONSEQUENTLY HUGE NO OF ITERATIONS ARE NECESSARY FOR FINDING THE VALUE OF VOLTAGE .

THIS IS HOW WE CAN MANUALLY SOLE FOR THE VALUE OF VOLTAGE .

NOW , BY MATLAB WE CAN WRITE THE CODE AS

x = 0;

temp = 1;

count = 0;

while x~= temp

 x = temp;

num = (0.004*x)+ 10.^(-15)*(exp(38*x)-1) -5;

demo = 0.004 + 38*(10.^(-15)*(exp(38*x)));

temp = x - (num/deno);

count = count+1;

p(count) = x;

end    

plot(p);

title('convergence after multiple iterations');

fprintf('No. of Iterations = '); disp(count);

fprintf('Answer =');disp(x);

THUS WE CAN USE MATLAB IN ORDER TO VERIFY NEWTON RAPHSON AND TO FIND THE UNKNOWN VALUE .IN OUR CASE IT IS THE VALUE IF VOLTAGE .

If you have any doubts you can write in the comments section .
By
Krishna Dubey
Satish Yadav