Question

The electric current i flowing in a device varies with time t. The equation linking the two variables is as follows.
i=2sin(5t)
The area under the graph represents the charge q that has passed over any given time interval.
Calculate the area and hence the charge by integrating the equation between t=t1 and t=t2
t1=0.4
t2=0.5

Answer 1

Answer on Question #58154-Engineering-Mechanical Engineering

The electric current is flowing in a device varies with time $t$. The equation linking the two variables is as follows.

$$i = 2 \sin (5t)$$

The area under the graph represents the charge $q$ that has passed over any given time interval.

Calculate the area and hence the charge by integrating the equation between $t = t1$ and $t = t2$

$$t1 = 0.4$$ $$t2 = 0.5$$

Solution

$$\Delta Q = \int_{t_1}^{t_2} i(t) \, dt = \int_{0.4}^{0.5} 2 \sin(5t) \, dt = \frac{2}{5} \int_{0.4}^{0.5} \sin(5t) \, d(5t) = \frac{2}{5} (-\cos 5t)_{0.4}^{0.5} = \frac{2}{5} (\cos 2 - \cos 2.5) \\ = 0.154 \, C.$$

Answer: $0.154 \, C$.

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