Question

若u=20√2sin(wt+60°)v,i=5√2sin(wt+15°)A,则Z为__Ω,该电路的功率为__W。

Answer 1

问：若u=20√2sin(wt+60°)v,i=5√2sin(wt+15°)A,则Z为__Ω,该电路的功率为__W。

答：您好，根据电动势定义，有：u = Z * i所以，Z = u / i = (20√2sin(wt+60°)) / (5√2sin(wt+15°)) = 4Ω

答：根据功率定义，有：P = u * i = (20√2sin(wt+60°)) * (5√2sin(wt+15°)) = 50 * sin(wt+60°) * sin(wt+15°) = 25 * (cos(45°)sin(wt+60°)sin(wt+15°) + sin(45°)cos(wt+60°)cos(wt+15°))

答：根据三角函数的基本性质，可以得到：P = 25 * (0.5sin(wt+60°+wt+15°) + 0.5cos(wt+60°-wt-15°))P = 25 * (0.5sin(2wt+75°) + 0.5cos(-30°))P = 25 * (0.5sin(2wt+75°) + 0.5*(√3/2))P = 12.5sin(2wt+75°) + 12.5所以，该电路的功率为 P = 12.5W + 12.5W = 25W。