If the derivative property of phasors is the multiplication of the phasor by jω, the integral property of phasors is division of the phasor by jω. Use phasors and these properties to find the sinusoids in each of the following:

(A) v2 (t) = (1/100) dvi(t)/dt + 20v1(t) and v1(t) = (a) vz(t) = 10 cos(100t + 90°) V
(B) i2(t) = 10 ∫[ i1(t)dt – 3i1(t)] and i1(t) = -4 cos(5t) A

An ideal otto cycle with air as the working fluid has a compression ratio of 8. the minimum and maximum temperatures in the cycle are 300 k and 1340 k. use constant specific heats at room temperature to determine (a) the amount of heat transferred to the air during the heat- addition kj/kg, (b) the thermal efficiency, and (c) the thermal efficiency of a carnot cycle ope limits. process, in rating between the same temperature