Question 4 [15 Marks) a. The voltage, v(t), across a capacitor varies with time, t, according...
The voltage across a 27-4F capacitor is given by the following function of time. V(t) = 200 sin(500t) V Find the value of the Power in Watts at timet -0.1. (The angle is in radians) v(t) = 200 sin(5000) i(t) с
2) (15 points) Consider a voltage signal v(t)Vocos(wt) (a) Consider applying v(t) across a capacitor C (i) What's the current into the capacitor? (ii) Plot the current and the voltage in the time domain and draw their respective phasors in the complex plane. (ii) Does the current lead or lag the voltage? Explain intuitively. (b) Repeat (i), (ii), and (ii) for part (a) but with an inductor, L, instead of a capacitor. (c) Repeat (i), (ii), and (ii) for part...
The initial voltage across the capacitor is 0 V. At time t=0, the switch is closed a) What is the time constant for this circuit? b) What is the final voltage across the 50 capacitor? c) What is the expression for the voltage across the 50 capacitor? d) Sketch the waveform for . e) What is the maximum instantaneous current that will flow through the capacitor? f) When will the voltage reach 5.0 V?
252 322 6480 0.25 E 4V /12V Question 11 1 pts 11. The voltage v across the capacitor fort > 0 2exp(-2t) [2cos(2t) - sin(2t)] V 2exp(-t) [2cos(2t) - sin(2t)] V 2exp(-t) (cos(2t) - 2sin(2t)] V 2exp(-t) [2cos(5t) - sin(5t)] V
Question 4 a) Differentiate with respect to x, i. y = sin 2x ii. y = x In(5x + 2) b) Show that if y = cotx, dy dx -cosec? x c) Show that if y = tan x, then dy dx 1 1+xal Question 5 Use calculus to find any turning points of the function A(t) = te-020 and determine their nature (maximum, minimum or inflexion) using any method. Question 6 a) Find tan” x dx b) Use integration...
QUESTION 2 Given the voltage across a 10 uF capacitor is v. = 200.t find the capacitor current (ic). ic = mA
The voltage across a parallel-plate capacitor with area A = 740 cm2 and separation d 7 mm varies sinusoidally as V (13 mV)cos(160t), where t is in seconds. Find the displacement current between the plates. (Use the following as necessary: t. Do not use other variables, substitute numeric values. Assume that I4 is in amperes. Do not include units in your answer.) I4 (0.000000000194598855) (sin(160t) X
The capacitor in the circuit is initially uncharged, when at t = 0 s, the switch is closed. At what time is the voltage across the capacitor equal to 7.5 V?
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1. Let r(t) = -i-e2t j + (t? + 2t)k be the position of a particle moving in space. a. Find the particle's velocity, speed and direction at t = 0. Write the velocity as a product of speed and direction at this time. b. Find the parametric equation of the line tangent to the path of the particle at t = 0. 2. Find the integrals: a. S (tezi - 3sin(2t)j +...
1. If a particle moves according to a law of motion S(t)=12-6-7, t 20 Where t is measured in seconds and sin meters, (a) Find the velocity of the particle in terms of t. (b) Find the velocity and the speed at time t=1. (c) When is the particle at rest? (d) When is the particle moving to the right and when is it moving to the left? (e) Find the acceleration of the particle at t. (10pts) 2. Evaluate...