Question

A certain electrical element draws the current
i(t) = 10 cos 4t A at a voltage v(t) = 120 cos 4t V.
Find the energy absorbed by the element in 2 s.

Answer 1

Given info : A certain electrical element draws the current i(t) = 10 cos 4t A at a voltage v(t) = 120 cos 4t V.

To find : the energy absorbed by the element in 2 sec is ...

solution : we know, Workdone, W = ∫i(t) × v(t) dt

= $\int\limits^2_0{10cos4t\times120cos4t}\,dt$

= $1200\int\limits^2_0{cos^2(4t)}\,dt$

= $1200\int\limits^2_0{\frac{1}{2}(1+cos8t)}\,dt$

= $600\left[t+\frac{sin8t}{8}\right]^2_0$

= 600[2 + sin16/8 ]

= 600 × 1.964

= 1178.4 J

the energy absorbed by the element in 2 sec is 1178.4 J.

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