The charge entering the positive terminal of an element is = 10 sin while the voltage across the element is = 2 cos (i) find the power delivered to the element at t = 0.3s. (ii) calculate the energy delivered to the element between 0 and 0.6s.

P (t = 0.3) = 164.5 mW

W ( 0 < t < 0.6) = 78.34 mJ

Explanation:

Given:

q (t) = 10*sin(4*pi*t) mC

V (t) = 2 *cos(4*pi*t) V

part a

The current i (t) flowing through the element is obtained as follows:

i (t) = dq / dt

= d (10*sin(4*pi*t)) / dt

= 40 * pi * cos (4*pi*t)  mA

Next P(t) delivered to the element is obtained as follows:

P (t)  = i (t)*V(t)

=  40 * pi * cos (4*pi*t) * 2 *cos(4*pi*t)

= 80*pi*(cos(4*pi*t))^2  mW

Finally the power delivered to element @ t = 0.3 s

P (t=0.3) = 80*pi*(cos(4*pi*0.3))^2 = 164.50 mW

P (t = 0.3) = 164.5 mW

part b

Energy delivered to the element time 0 to 0.6 s is obtained as follows:

W ( 0 < t < 0.6) = 78.34 mJ

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