Question

The charge entering the positive terminal of an element is q = 5 sin 4 π t mC while the voltage across the element (plus to minus) is v = 3 cos 4 π t V

(a) Find the power delivered to the element at t = 0.3 s.
(b) Calculate the energy delivered to the element between 0 and 0.6 s.

Answer 1

a)123.37 mW

b) 58.75 mJ

Step-by-step explanation:

a) The current (i) flowing through the terminal is given as:

`i=(dq)/(dt) \\i=(d(5sin(4\pi t))/(dt) =20\pi cos(4\pi t)\ mA\\`

The Power delivered to the element (P(t)) is given as:

`P(t)=v(t)i(t)= 3 cos(4\pi t)*20\pi cos(4\pi t)*10^(-3)\\P(t)=60\pi cos^2(4\pi t)*10^(-3)\\at \ t \ =\ 0.3s,\ the \ power\ delivered\ is:\\P(0.3) = 60\pi cos^2(4\pi *0.3)*10^(-3)=123.37mW`

b) the energy delivered to the element (W) between 0 and 0.6 s is given as:

`W = \int\limits^0_(0.6) {P(t)} \, dt \\W=\int\limits^0_(0.6) {60\pi cos^(2)(4\pi t)} \, dt =58.75mJ`