a non -inductive resistor is connected in series with a capacitor of 100micro farads cap. across 200v,50 hz mains .the pot diff across the resistor is 150v .find the value of resistance &the value of current taken from the mains if the resistor were connected in ||
with the capacitor instead...
use green lemma to evaluate line integral int of (x^2-y^2)dx-4xydy over rgn bounded by y^2=4x,y=0,x=1 in ist quadrant.
attempt
double integral (dv/dx -du/dy)dx dy=int. from limit 0to 2(int.from 0to 2x^1/2(6ydxdy))
=int.lim 0to 2(12x^3/2)dy
=24/5(2^5/2)
ans in book is -2.
if u(x,t)=ae^-gx sin(nt-gx) where A,g and n are const.,and partial derivative of u w.r.t t=
a^2[(partial derivative w.r.t x(partial derivative of u w.r.t x)] show :(1/a)[n/2]^1/2=g
given that z=[x^2 tan^-1(y/x)]-[y^2 tan^-1(x/y)].find value of [z][xy].
where [z][xy] stand for partial derivative w.r.ty(partial derivative of z w.r.tx)