In a simple AC circuit shown on the right, R = 75 Ohm, DeltaV = DeltaV_maxsin(om

Question

In a simple AC circuit shown on the right, R = 75 Ohm, DeltaV = DeltaV_maxsin(omegat) whee DeltaV_max = 9.5 V, and omega = 55 rad/s. Randomized Variables R = 75Ohm DeltaV_max = 9.5 V omega = 55 rad/s 11% Part (a) Express the current I in terms of t, R, DeltaV_max, and omega. 11% Part (b) Express the maximum of the current, I_max, in terms of DeltaV_max and R. 11% Part (c) Calculate the numerical value of I_max in amps. 11% Part (d) How long (in seconds) does it take for the current I to reach I_max (and be moving in the same direction) from the previous I_max? 11% Part (e) Express the power dissipated in the circuit, P, in terms of I and DeltaV. 11% Part (f) Express the power dissipated in the circuit, P, as a function of time t and R, DeltaV_max, and omega. 11% Part (g) Express the maximum of P, P_max, in terms of R and DeltaV_max. 11% Part (h) Calculate the numerical value of P_max in watts. 11% Part (i) How long does it take for the power P to reach P_max from the previous P_max in seconds.

Explanation / Answer

(a)

I = del V/R = Vmax sin wt/R

(b)

I _max= V_max/R

(c)

I_max = 9.5/75 = 0.126 A

(d)

I = Imax ( e^-t/R)

(e)

P = del V I

(f)

P= del V^2/R

P =(Vmax sin wt)^2/R

(g)

Pmax = (del V max)^2/R

As per guide lines I worked first four parts of the problem

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