Give expression for the average value of the a.c. voltage `V=V_0 sin omega t` over the time interval `t=0 and t=pi/omega`.

The equation of an a.c. voltage is V = 200 sin 50 pi t Then, the r.m.s. value of voltage is

For any arbitrary motion in space, which of the following relations are true :- v(t)=v(O)+a t (The ‘average’ stands for average of the quantity over the time interval t_1 to t_2 )

A voltage V = V_0 sinomegat is applied to a series LCR-circuit. Derive the expression for the average power dissipated over a cycle. Under what condition maximum power is dissipated in the circuit?

A voltage V = V_0 sinomegat is applied to a series LCR-circuit. Derive the expression for the average power dissipated over a cycle. Under what condition no power is dissipated even though the current flows through the circuit.

For any arbitrary motion in space, which of the following relations are true :- a_averag[v(t_2)-v(t_1)]/(t_2-t_1) (The ‘average’ stands for average of the quantity over the time interval t_1 to t_2 )

For any arbitrary motion in space, which of the following relations are true :- v_average=(1/2) (v(t_1))+(v(t_2)) (The ‘average’ stands for average of the quantity over the time interval t_1 to t_2 )

For any arbitrary motion in space, which of the following relations are true :- r(t)=r (O)+v(O) t+(1/2) a t^2 (The ‘average’ stands for average of the quantity over the time interval t_1 to t_2 )

The velocity-time graph of particle in one dimensional motion is shown in the fig. Which if the following formulae are correct for describing the motion of the pawrticle over the time interval t_1 to t_2 v(t_2) = v(t_1) + a(t_2 - t_2) , v_(average) = ([x(t_2) - x(t_1)])/((t_2 - t_1)) , x(t_2) - x(t_1) = area under the v - t curve. bounded by the t-axis and the dotted line shown.

For any arbitrary motion in space, which of the following relations are true :- v_average=[r(t_2)-r(t_1)/(t_2-t_1) (The ‘average’ stands for average of the quantity over the time interval t_1 to t_2 )

An a.c. voltage E = E_0 sin omegat is applied across an inductance L. Obtain an expression for the current in the circuit and hence obtain the phse of the current flowing w.r.t the applied voltage.