The current at time t in a coil with resistance R inductance L and subjected to a constant electromotive force E is given By `I = (E )/(R ) (1- e^((-Rt)/(L)))` obtain a suitable formula to be used where R is small.

The equation of electromotive force for an electric circuit containing resistance and self inductance is E=Ri+L (di)/(dt) , where E is the electromotive force is given to the circuit, R the resistance and L, the coefficient of induction. Find the current i at time t when E = 0.

Plot a graphs showing the variation of circuit I varisous resistance R connected to a cell of emf E and internal resistance r.

An ac voltage is applied to a resistance R and inductor L in series If R and the inductive reactance are both equal to 3Omega the phase difference between the applied voltage and the current in the circuit is :

The charge flowing through a resistance R varies with time t as Q= at-bt^2 , where a and b are positive constants. The total heat produced in R is

Spherical rain drop evaporates at a rate proportional to its surface area. The differential equation corresponding to the rate of change of the radius of the rain drop if the constant of proportionality is K >0 is (a) ( b ) (c) (d)(( e ) dy)/( f )(( g ) dt)( h ) (i)+K=0( j ) (k) (b) ( l ) (m) (n)(( o ) d r)/( p )(( q ) dt)( r ) (s)-K=0( t ) (u) (c) ( d ) (e) (f)(( g ) d r)/( h )(( i ) dt)( j ) (k)=K r (l) (m) (d) None of these

A coil having an inductance L and a resistance R is connected to a battery of emf epsilon . Find the time elapsed before (a) the current reaches half its maximum value, (b) the power dissipated in heat reaches half its maximum value and © the magnetic field energy stored in the circuit reaches half its maximum value.