00:01
In this problem we have a circuit and the switch is in position a and we have to find out the value of r for which the circuit will have time constant of 15 .0 microseconds.
00:18
So when the switch is in position a, the circuit has an inductance and two resistors in parallel.
00:39
The resistors are 450 ohms and r.
00:46
Now the equivalent resistance of the circuit will be equal to the parallel combination of the two resistors.
00:54
So it is r times 450 ohm upon r plus 450 ohms and the time constant is equal to the inductance of the circuit upon the equivalent resistance.
01:13
Now from this we get the equivalent resistance equal to inductance upon time constant.
01:24
Now equivalent resistance is r times 450 ohms upon inductance is 5 .00 millihenry which is 5 .00 times 10 to the power minus 3 seconds and time constant is 15 .0 microseconds which is 10 to the power minus 6 seconds.
01:52
The inductance has unit of henry.
01:59
Now from this we get 450 r upon r plus 450 equal to 1000 upon 3.
02:11
So 3 times 450 r is equal to 1000 r plus 450, 1000.
02:26
So 3 times 450 minus 1000 r is equal to 350.
02:33
So 350 r is from this we get the resistance equal to 1 .29 times 10 to the power 3 ohms and 10 to the power 3 is 1000 and 1000 ohm is kilo ohm.
02:55
So in kilo ohms it can be written as 1 .29 kilo ohms...