00:01
Hello student, in this problem an industrial coil is given which have the circuit, which have the circuit, a resistor, r, and the coil has the series combination of r, an inductor l, connected across a synestolar voltage source vs, and the voltage across this register is v1, the value of register is 80 -oom, the resistance is a transistor, and the resistance is, is r and this is inductance l and the value across this is v0, this is a coil, okay? this is the coil.
00:55
And the frequency of the system is f equals to 60 hertz, f equals 60 hertz and input voltage vs equals to 145 volt, vs equals to 145 volt and v1 equals to v1 equals to v1 equals to 50 volt and v0 or output voltage across the coil is 110 volts.
01:23
So now we have to measure the value of unknown parameter of coil, register r and inductor l in this circuit.
01:35
So here we know that our system voltage vs equals to 145.
01:41
It is a sinusoidal voltage source.
01:44
It is a sinusuter voltage source.
01:46
So it can write 145 angle of 0 degree.
01:51
And in case of inductor, in case of inductor, we know that xl equals to omega -l equals to 2 pi into frequency f.
02:05
Frequency f it is it is 60 harts into l then the inductance xl equals to 377 l is clear so now we have to find out the value of r and l so in this problem first we have to calculate the voltage across the source voltage across the register ato so v1 equals to let assume the current in the circuit is i then v1 equals to 80 into i, v1 equals to 80 into i.
02:45
So here first we have to calculate the current, okay? so first we have to calculate the current.
02:51
Then i equals to simply v upon z, i equal to simply v upon z, then i equals to i equals to v is 145 angle 0 degree upon z is the series combination of all these elements then it give 80 plus r plus iota xl xl represent the inductive reactants okay xl represent the inductive reactants okay so this is the equation number first so now so now v1 equals to v1 equals to 80, multiply by 145, ignoring the angle, why because of it is 0 degree, upon 80 plus 80 plus r plus aorta excel.
03:54
So what about the v1? v1 is simple 50.
04:01
So 50 equals to 80 into 145 upon 80 plus r plus iota xl.
04:16
Equation number second.
04:19
Okay.
04:19
And now we have to calculate the value of the value across the output circuit.
04:28
Then it is v0.
04:30
Okay.
04:31
So v0 equals to, v0 equals to same v equals to same i into z, i into z, then v not equals to i and what about the z? r plus iota xl because a register and inductor are connected in series, then v0 equals to what about the i or i will be this one? then it gives 1 .45 upon 80 plus r plus iota xl multiply r plus iota xl.
05:17
Okay, so now v0 equals to and what about the v note? we have the value of v0.
05:27
Then the value of v0 is 110.
05:31
110 equals to r plus iota xl 145 upon 80 plus r plus iota xl 145 upon 80 plus plus r plus iota xl equation number 3 it is clear now from equation second and third from equation from equation from equation second and third we have to divide these equation then it give 50 upon 110 equals to equals to if you divide these two functions, then 80 plus r plus xcel and this function are cancel out and 145 to 145 is also cancel out, then it gives 80 upon in this term r plus iota xl.
06:48
It is clear.
06:49
Now by cross multiplying this, by cross multiplying this it gives r plus iota xl equals to 80, 80 into 110 upon 50.
07:11
So now r squared plus xl square equals to 30976 equation number 4.
07:23
It is clear, it is clear...