Tok kuchining o'zgarish qonuni berilgan shaklda: I = cos(10 t)

Tok kuchining o'zgarish qonuni berilgan shaklda: i = 5cos(10^7 * t).
Kondensatorning zaryadi (Q) va tok kuchi (i) orasidagi aloqani foydalanib, zaryadning qiymatini topishimiz mumkin. Zaryadning qiymati, integralli olinadi:
Q = ∫ i dt.
Bu yerda integrallashning chegarasi vaqt oralig'ida bo'lgan daraja (0 dan t gacha) bo'ladi.
Q = ∫[0 to t] 5cos(10^7 * t) dt.
Integralni hisoblash uchun trigonometrik integrallash formulasidan foydalanamiz. Quyidagi formula yordamida integrallashni amalga oshiramiz:
∫ cos(a * t) dt = (1 / a) * sin(a * t) + C.
Bu yerda C ko'rsatkich integrallashning integralli muhim ko'rsatkichi emas, chunki u yerga kelgan qiymatning 0 ga teng bo'lishi kerak.
Shunday qilib, integrallashni amalga oshirish:
Q = (1 / (10^7)) * sin(10^7 * t) |[0 to t].
Q = (1 / (10^7)) * (sin(10^7 * t) - sin(0)).
Q = (1 / (10^7)) * (sin(10^7 * t) - 0).
Q = (1 / (10^7)) * sin(10^7 * t).
Demak, zaryadning maksimal qiymati, t = π / (2 * 10^7) ga teng bo'lganida bo'ladi:
Q(max) = (1 / (10^7)) * sin(10^7 * (π / (2 * 10^7))).
Q(max) = (1 / (10^7)) * sin(π / 2).
Q(max) = (1 / (10^7)) * 1.
Q(max) = 10^-7=1 µC
Shunda maksimal zaryad qiymati 1 mikrokulomb (µC) ga teng bo'ladi