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Introducing Epsilon

40.The averag...

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40.The average value of sawtooth voltage V=V^°{2t/T-1} over 0 to T/2 is given by

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Q. The voltage over a cycle varies as

V = V_{0} s i n ω t f o r 0 \leq t \leq \frac{π}{ω}

V = - V_{0} s i n ω t f o r \frac{π}{ω} \leq t \leq \frac{2 π}{ω}

Then the average value of voltage is

Q. The voltage supplied to a circuit is given by

V = V_{0} t^{3 / 2}

t

is time in second. Find the

r m s

value of voltage for the period,

t = 0

t = 1 s

Q. For a given A.C voltage

V = V_{0} sin ω t

V_{1}

is average voltage of half cycle and

V_{2}

is rms voltage, then

\frac{V_{1}}{V_{2}}

Q. The rms value for the saw-tooth voltage of peak value

V_{0}

t = 0

t = 2 T

as shown in the figure is

\frac{V_{0}}{\sqrt{x}}

. Find the value of

x

.

Q. For any arbitrary motion in space, which of the following relations are true : (a) v _average = (1/2) (v (t₁) + v (t₂)) (b) v _average = [r(t₂) - r(t₁) ] /(t₂ – t₁) (c) v (t) = v (0) + a t (d) r (t) = r (0) + v (0) t + (1/2) a t₂ (e) a _average =[ v (t2) - v (t₁ )] /( t₂ – t₁) (The ‘average’ stands for average of the quantity over the time interval t₁to t2)

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