A sinusoidal voltage ?v = 35.0 sin(100t), where ?v is in...

A sinusoidal voltage ?v = 35.0 sin(100t), where ?v is in volts and t is in seconds, is applied to a series RLC circuit with L = 150 mH, C = 99.0 µF, and R = 72.0 ?. (a) What is the impedance (in ?) of the circuit? ? (b) What is the maximum current (in A)? A (c) Determine the numerical value for ? (in rad/s) in the equation i = I_max sin(?t - ?). rad/s (d) Determine the numerical value for ? (in rad) in the equation i = I_max sin(?t - ?). rad (e) What If? For what value of the inductance (in H) in the circuit would the current lag the voltage by the same angle ? as that found in part (d)? H (f) What would be the maximum current (in A) in the circuit in this case? A

Transcript

00:01 Here we have a series rlc circuit and this series rlc circuit is connected to a 35 volt 100 radial per second supply.

00:11 Here 35 is the maximum value of supply voltage.

00:14 Here we take this supply voltage as a reference voltage, that's why we write delta v is equal to 35 angle 0 degree.

00:23 Here delta v is equal to 35 angle 0 degree is the phager form representation of this time domain voltage signal.

00:29 Now suppose maximum current flowing through the circuit is equal to i.

00:34 Now inductive reactance of this circuit is given by xl is equal to omega l.

00:40 Here omega is equal to 100 and l is equal to 150 into 10 to the power negative 3 and from this we obtain xl equals to 15 om.

00:50 Now next capacity reactance of the circuit is given by xc is equal to 1 over omega into c, omega is equal to 100.

01:00 And here c is equal to 99 into 10 to the power negative 6 and from this we obtain xc is equal to 101 .01 om.

01:15 Now suppose total impedance of the circuit is equal to z.

01:20 So the value of z is given by r plus j xl minus x c.

01:28 Here r is equal to 72 plus j x x.

01:29 Here r is equal to 72 plus j x l is equal to 15, x is equal to 101 .01.

01:40 From this we obtain z is equal to 72 minus z 86 .01 om.

01:52 In the rectangle form, the value of z is equal to 112 .16 .3 angle negative 50 .0667 degree om.

02:03 Now the maximum current flowing through the circuit is given by i is equal to delta v over z delta v is equal to 35 angle 0 over z is equal to 112 .16 a 3 angle negative 50 .0667 and by simplifying this we obtain i is equal to 0 .312 angle 50 .0667 degree ampere from this we obtain i max equals to 0 .312 ampere here this is the maximum current in the phageiform and this is the maximum current.

02:46 Now this current in the time domain is given by it is equal to 0 .312 sine 100t plus 50 .067 degree.

03:08 So for this current, omega is equal to 100 radian per second.

03:15 Now by comparing this equation and this equation we obtain the value of 5 is equal to negative 50 .067 degree.

03:31 And in the radian, we obtain 5 is equal to 50 .067 into pi over 180...

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