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Give expression for average value of a.c...

Give expression for average value of a.c. voltage `V = V_(0) sin omega t` over interval `t = 0` to `t = (pi)/(omega)`

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To find the average value of the alternating current (a.c.) voltage given by the equation \( V = V_0 \sin(\omega t) \) over the interval from \( t = 0 \) to \( t = \frac{\pi}{\omega} \), we can follow these steps: ### Step 1: Understand the Function The given voltage function is \( V(t) = V_0 \sin(\omega t) \). This is a sinusoidal function, where \( V_0 \) is the peak voltage and \( \omega \) is the angular frequency. ### Step 2: Identify the Interval We need to calculate the average value of this function over the interval from \( t = 0 \) to \( t = \frac{\pi}{\omega} \). This interval represents half of the time period of the sinusoidal function, since the time period \( T \) is given by \( T = \frac{2\pi}{\omega} \). ...
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What is the average value of atlernating current, I = I_(0) sin omega t over time interval t = pi//omega to t = pi//omega ?

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Knowledge Check

  • The average value of a.c. voltge E =E_(0) sin omega t over the time interval t = 0 to t = pi//omega is

    A
    `- 2 E_(0)//pi`
    B
    `E_(0)//pi`
    C
    `(2 E_(0))/(pi)`
    D
    zero

  • The average value of an alternating voltage V=V_(0) sin omega t over a full cycle is

    A
    `V_(0)`
    B
    `(V_(0))/(Sqrt(2))`
    C
    `(2V_(0))/(pi)`
    D
    Zero

  • The average value of alternating current I=I_(0) sin omegat in time interval [0, pi/omega] is

    A
    `(2I_(0))/pi`
    B
    `2I_(0)`
    C
    `(4I_(0))/pi`
    D
    `I_(0)/pi`

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