Question

Problem 1.20 The voltage and current at the terminals of the circuit element in (Figure 1) are zero fort < 0. u= (1500t + 1)e 750t V t> 0; i= 70e 7500 mA, t> 0. Part A where t is in seconds Find the time (in milliseconds) when the power delivered to the circuit element is maximum. Express your answer using three significant figures. t = 0 ms Submit Previous Answers Correct Part B Find the maximum value of p in milliwatts. Express your answer using three significant figures. Pmax = 70.0 mW Submit Previous Answers Correct Part C Find the total energy delivered to the circuit element in microjoules. Express your answer using three significant figures. IVO ALOJfvec ? Figure < 1 of 1 > Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining 1 Provide Feedback V 2

Answer 1

For the given current and voltage equations, the required values are calculated as below :

Given v = (150 ot + l)e 9- WA to. So As both terms have exponential (megative) values, it is maximum at pereer delivered is maximem if - Omsee ho Evi = [ (1500(0) + 1) e ] [ to eo I mw (1)(70) mw maximum 90 Р To mW Value, Total energy - 150 Spat Suidt. 15006 +1] 2 4506} { sat} de s [1soot e 1Sootjdt 70 1000 - 1500 - Isoot 1000 -15oot [a + 1500 t] dt 0.07

W = 0.07 -15oot [1 + 1500t] dt W= 0.07. - 1500t 1500t of + oin (1500 ) WE 0.07 1500+ + de (isant) de 0.07 { into a fare" comedy 1500 As eo and = 0.07

Value of second integral is calculated using integration byparts.

For the second integral Using integration by parts, 1500 f te -15oot -1500t - 1500t dt 150 - t 1500 1500 O - 1500t 1500 x 1500 -1500 2 1 500k ] Isco [o-1] - 1500 = [o-o

So the energy is calculated as :

so, useof 1500 - 1500t t e 2 dt 0 1500 so, we 1 2 0.01 + 1500 1500 0.07 { U 750 W = 0.933 l Joule

So the value of energy is as above.