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Hello.
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For part a of this question we have to calculate the rms current.
00:05
For that, first the angular frequency of the circuit can be calculated as omega is equal to 2 pi f equals 2 pi into f is 240 by pihertz.
00:19
So it equals 480 radian per second.
00:24
Now the inductive reactants of the circuit can be calculated as xl is equal to l omega.
00:32
Equals la 0 .1 henry into 480 radiant per second equals 48 om.
00:41
Now the capacity reactants of the circuit can be calculated as xc equals 1 by c omega.
00:50
Here the value of c is equal to 40 micro -faird.
00:56
In ferret it can be written as equal to 40 into 10 -2 minus 6 ferret.
01:02
We can substitute the values equals 1 divided by 40 into 10 raised to minus 6 into 480 radiance per second equals 52 .083 om.
01:21
Now the rms current through the circuit can be written as irms equals v divided by z.
01:29
Here z is the impedance of the circuit.
01:32
Again the rms current can be written in terms of the resistance of the resistor as irms equals vr divided by r.
01:43
Here r is the resistance of the resistor.
01:46
Now let's equate these two equations so we can write vr by r equals v by z.
01:56
Let's square both sides of this equation.
01:59
Hence we get vr square divided by a.
02:02
R square equals v square divided by z square.
02:09
Now the impedance of the circuit can be written as z is equal to root of r square plus xl minus xc the whole square.
02:23
We can square both sides of the equation.
02:25
So we get z square equal to r square plus xl minus xc the whole square.
02:34
Now let's insert this equation for z square here in this equation...