2. For the circuit shown below, V = 10∠ 20^∘ V and i = 10∠ 90^∘ mA at ω = 10^5 rad/s. If theis i

Step 1: The circuit is in steady state, so the capacitors act as open circuits and the inductor

2. For the circuit shown below, V = 10∠ 20^∘ V and i = 10∠...

2. For the circuit shown below, $V = 10\angle 20^\circ V$ and $i = 10\angle 90^\circ mA$ at $\omega = 10^5 rad/s$. If the\ncircuit is in steady state, find the current $i(t)$ through the inductor.

Transcript

00:01 5 in the given problem there is a series rcl circuit in which the value of resistance is given as 108 oam the capacitance is 0 .2002 micro ferret and the self -inductance is 5 .42 millie henri rms voltage apply is 26 .0 volt and rms current obtained is also given to us which is 0 .141 am here.

00:48 So using om's law we can find the impedance of the given rcl circuit.

00:59 So that impedance will be z is equal to ratio of rms voltage to the rms current.

01:11 This is 26 .0 volt divided by 0 .141 ampere and it comes out to be 184 .4.

01:23 The frequency of this source, alternating current source, is a is missing we have to find that frequency for which the expression for the impedance z is equal to square root of net reactance xl minus xc to the whole square plus r squared and this is first case when inductive reactance is more than capacitive reactance but the same impedance may be possible at a value of xc which is more than xl means xc minus xl squared plus r square.

02:10 In that case, actually we will have two values of the frequency in order to get the same rms current.

02:19 First case when xl is more than xc and second case when xc is more than xl.

02:25 So we are using the first case when xl was more than xc.

02:33 So, making a square of both the sides of this expression for the impedance, we get z square is equal to xl for xl, this is 2 .5 fl, minus xc for which this is 1 by 2xc, to the whole square plus r square.

02:57 Hence plugging in all other values and rearranging the term.

03:03 Comes also this is square of the bracket will be 2 pi f frequency is missing for l this is 5 .42 millie henry or 5 .42 into 10 dash per minus 3 henry minus 1 by 2 pi f c 1 by 2 pi f sequence is missing again 0 .2 micro ferret or 0 .2 into 10 dash minus 6 pharret to the whole square is equal to z square minus r square and for z square this is hundred and eighty four point four to the whole square minus r square means hundred and eight to the whole square so this is three four zero zero three point three six minus one one six six four so finally it comes out to be two 2 .339 .36.

04:07 And here if we solve these terms here, this is 34 into 10 dashpar minus 3 to f minus 796178.

04:23 0 .3 divided by f and it will be square root of this.

04:31 So, finally this is 149 .5.

04:36 Now, on multiplying both of the sides by f and non -frequency, here it becomes 34 into 10 dash power minus 3, f squared, minus 796178 .3 is equal to 149 .5 f...

Question

2. For the circuit shown below, $V = 10\angle 20^\circ V$ and $i = 10\angle 90^\circ mA$ at $\omega = 10^5 rad/s$. If the\ncircuit is in steady state, find the current $i(t)$ through the inductor.

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