A Resistance of 100 Ohms and Inductance of 0.5 Henries Are Connected in Series with a Battery of 20 Volts. Find the Current at Any Instant If the Relation Between L,R,E is L D I D T + R I = E - Applied Mathematics 2

Advertisements
Advertisements
Sum

A resistance of 100 ohms and inductance of 0.5 henries are connected in series With a battery of 20 volts. Find the current at any instant if the relation between L,R,E is L `(di)/(dt)+Ri=E.`

Advertisements

Solution

L`(di)/(dt)+Ri=E.`

`therefore (di)/(dt)+(Ri)/L=E/L`

Solution is given by ,

`i,e^(int(R/L)dt=inte^(int(R/L)dt)E/Ldt+c`

`therefore"i".e^((Rt)/L)=(Ee^((Rt)/L))/R+c`

At t = 0, i = 0 `thereforec=E/R`

`therefore "i".e^((Rt)/L)=(Ee^((Rt)/L))/R+(-E)/R`

`therefore "i" = E/R(1-e^(-(Rt)/L))`

For given condition R = 100, L = 0.5, E = 20

`therefore i=0.2(1-e^(-200t))`

Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
  Is there an error in this question or solution?
2017-2018 (June) CBCGS

RELATED QUESTIONS

Evaluate `(d^4y)/(dx^4)+2(d^2y)/(dx^2)+y=0`


Evaluate `(2x+1)^2(d^2y)/(dx^2)-2(2x+1)(dy)/(dx)-12y=6x`


Solve `(D^3+1)^2y=0`


Solve `(D^3+D^2+D+1)y=sin^2x`


Solve the ODE `(D-1)^2 (D^2+1)^2y=0` 

 

 


Evaluate `int_0^1 int_0^(x2) y/(ex) dy  dx` 


Evaluate `int_0^1( x^a-1)/log x dx` 

 


Solve `(1+x)^2(d^2y)/(dx^2)+(1+x)(dy)/(dx)+y=4cos(log(1+x))`


Find the length of cycloid from one cusp to the next , where `x=a(θ + sinθ) , y=a(1-cosθ)`


Solve `(D^2-3D+2) y= 2 e^x sin(x/2)`


Using D.U.I.S prove that `int_0^∞ e^-(x^+a^2/x^2) dx=sqrtpi/2 e^(-2a), a> 0` 


Solve `(D^2+2)y=e^xcosx+x^2e^(3x)`


Evaluate `int_0^1int_0^( 1-x)1int_0^( 1-x-y)     1/(x+y+z+1)^3 dx dy dz` 

 


Find the mass of the lemniscate π’“πŸ=π’‚πŸπ’„π’π’” 𝟐𝜽 if the density at any point is Proportional to the square of the distance from the pole . 


Solve`  x^2 (d^3y)/dx^3+3x (d^2y)/dx^2+dy/dx+y/x=4log x` 

 


Solve `(D^2-7D-6)y=(1+x^2)e^(2x)`


Apply Rungee Kutta method of fourth order to find an approximate Value of y when x=0.4 given that `dy/dx=(y-x)/(y+x),y=1` π’š=𝟏 π’˜π’‰π’†π’ 𝒙=𝟎 Taking h=0.2. 


Solve by variation of parameters` ((d^2y)/dx^2+1)y=1/(1+sin x)`


Compute the value of `int _0.2^1.4 (sin  x - In x+e^x) ` Trapezoidal Rule (ii) Simpson’s (1/3)rd rule (iii) Simpson’s (3/8)th rule by dividing Into six subintervals. 


Evaluate `int_0^(a/sqrt2) int_y^(sqrt(a2-y^2)) log (x^2+y^2) "dxdy by changing to polar Coordinates".` 


Evaluate `int int int  x^2` `yzdzdydz`over the volume bounded by planes x=0, y=0, z=0 and `x/a+y/b+z/c=1`


Evaluate `int_0^inftye^(x^3)/sqrtx dx`


Find the length of the curve `x=y^3/3+1/(4y)` from `y=1 to y=2`


Solve `(D^2+D)y=e^(4x)`  


Evaluate `int_0^1 int_(x^2)^x xy(x+y)dydx.`


Solve `(4x+3y-4)dx+(3x-7y-3)dy=0`


Solve `dy/dx=1+xy` with initial condition `x_0=0,y_0=0.2` By Taylors series method. Find the approximate value of y for x= 0.4(step size = 0.4).


Solve `(d^2y)/dx^2-16y=x^2 e^(3x)+e^(2x)-cos3x+2^x`


Show that `int_0^pi log(1+acos x)/cos x dx=pi sin^-1 a  0 ≤ a ≤1.` 


Evaluate `int int int (x+y+z)` `dxdydz ` over the tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + y + z = 1.


Find the mass of lamina bounded by the curves π’š = π’™πŸ − πŸ‘π’™ and π’š = πŸπ’™ if the density of the lamina at any point is given by `24/25 xy` 


In a circuit containing inductance L, resistance R, and voltage E, the current i is given by `L (di)/dt+Ri=E`.Find the current i at time t at t = 0 and i = 0 and L, R and E are constants.


Share
Notifications



      Forgot password?
Use app×