0:00
Hi.
00:02
To find the accurate integral expression for i of p, we can start by plugging in the values of sigma and omega in the given equation of i of p.
00:12
That is, i of t is equal to 1 by l omega, e rise to minus sigma t multiplied by omega, kose omega t minus sigma t, sine, omega t v t where l omega and sigma are defined as sigma is equal to r by 2 l omega is equal to square root of r by 2l the whole square minus 1 by lc find the accurate integral for i of t substituting these values into the expression of i of t we get i of t is equal to 1 by l omega we raise to minus sigma t multiplied by omega cos omega t minus sigma sine omega t d t.
01:23
Integrating this expression with respect to t we get i of t d t is equal to 1 by l omega integral e -raise to minus sigma t multiplied by omega cos omega t minus sigma sine omega t d t using integration by parts we can simplify this expression as integral i of t d t is equal to 1 by l omega into e -raise to my minus sigma t into sine omega t divided by omega plus cos omega t multiplied by sigma by omega square plus c where c is the constant of integration to find the value of current after 5 milliseconds we can simply plug in t is equal to 0 .005 seconds into the expression for i of t.
02:42
Calculating sigma is equal to r by 2l, which is equal to thousand divided by 20 .47, which is equal to 10 ,638 .3.
02:59
Also, omega, which is obtained from the expression r by 2l, the whole square minus 1 by l...