The complex expression 250ej25∘ejωt or 250∠25∘ejωt accurately represents the given alternating current i = 250sin (ωt + 25°) A, using Euler's formula and the concept of phasors to combine amplitude, phase, and time dependence into a concise complex form.

The given alternating current (AC) expression is i = 250 sin (ω t − 25 ∘), where i is the current in amperes, 250 is the amplitude of the current, ω is the angular frequency in radians per second, t is the time in seconds, and Show more…

The complex expression for a given alternating current, \ ( i = 250 \sin (\omega t - 25^\circ) \), can be represented using Euler's formula. Euler's formula states that @$\begin {align*}e^ {ix} = \cos (x) + i\sin (x)\end {align*}@$.

The peak value of the voltage is the maximum value of the voltage function, which is 250. The RMS value of the current can be calculated in a similar way by finding the peak value of the current function.

Question: A complex voltage given by: v = 250 sin (wt) + 50 sin (3wt + 3) + 20 sin (5wt + 577 + is applied to a series circuit of resistance 20 ohm and inductance 0.05 H. Take w = 314 rad/s. Determine the following: (a) Derive an expression for the current. (b) Rms value of the voltage. (c) Rms value of the current.

2 We can rewrite the expression in the form of a complex number using Euler's formula: + 250 ⁡ ( − 2) = + 250 ( sin ⁡ w t cos ⁡ − cos ⁡ w t sin ⁡) I+250\sin (wt-25^\circ)=I+250\left (\sin wt\cos 25^\circ - \cos wt\sin 25^\circ\right) I+250sin(wt−25∘)=I+250(sinwtcos25∘−coswtsin25∘)

2018年9月15日 · However, what I do not understand is why sin (wt) [I know omega is the letter used but I only have w on my keyboard] is used instead of sin (t). It is time which is plotted on the horizontal axis, so surely the y-axis represents displacement (x) …