What is the sum of the instantaneous current | vedclass

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(A) The instantaneous current in an $AC$ circuit is given by $I(t) = I_{max} \sin(\omega t)$.To find the sum (or integral) of the instantaneous curren

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(A) The instantaneous current in an $AC$ circuit is given by $I(t) = I_{max} \sin(\omega t)$.To find the sum (or integral) of the instantaneous current values over one complete cycle of period $T$,we calculate the integral $\int_{0}^{T} I(t) dt$.$\int_{0}^{T} I_{max} \sin(\omega t) dt = I_{max} [-\frac{\cos(\omega t)}{\omega}]_{0}^{T}$.Since $\omega = \frac{2\pi}{T}$,we have $\omega T = 2\pi$.Substituting the limits: $I_{max} [-\frac{\cos(2\pi)}{\omega} - (-\frac{\cos(0)}{\omega})] = I_{max} [-\frac{1}{\omega} + \frac{1}{\omega}] = 0$.Therefore,the sum of the instantaneous current values over one complete $AC$ cycle is $0$.

What is the sum of the instantaneous current values over one complete $AC$ cycle?

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