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

Answer 1

The power delivered to the element at t = 0.3 s is approximately 7.5 mW.

Step-by-step explanation:

The power delivered to the element can be found using the formula P = IV, where P is the power, I is the current, and V is the voltage. Since the current and voltage formulas are given as sinusoidal functions, we can use the trigonometric identity cos(θ) = sin(θ + π/2) to find the power as a function of time.

At t = 0.3 s, the current is given by I = Im sin(2πft), where Im is the current amplitude and f is the frequency. Plugging in the values, we get I = 5 sin(4π(0.3)) mC. The voltage is given by V = Vm cos(2πft), where Vm is the voltage amplitude. Plugging in the values, we get V = 3 cos(4π(0.3)) V.

Now, we can find the power by multiplying the current and voltage expressions: P = IV = (5 sin(4π(0.3)))mC * (3 cos(4π(0.3)))V = 15 sin(4π(0.3)) cos(4π(0.3)) mC * V = 7.5 sin(4π(0.3) + π/2) mC * V. Plugging in the values, we get P ≈ 7.5 mC * V = 7.5 mW.