Problem-1
Let be the angular frequency of the supply voltage.
Given details are
Now the inductive reactance will be
(a)
Since the three components are connected in series, the equivalent impedance of the circuit will be
The magnitude of the equivalent impedance will be given as
(b)
Let be the angular frequency at which
(c)
The equivalent impedance at the frequency of is
Given the peak-to-peak voltage is
So, the RMS voltage is
So, the phasor representation of the source voltage is given as
The current through the circuit will be
The voltage drop across the resistor is
So, the peak-to-peak voltage across the resistor is
By observing the expression for the line current it is evident that the current lags the source voltage by 45 degrees.
Problem-2
Given details are
the resonant frequency is given by
At the resonant frequency, we have
The impedance of the circuit will be given by
The current through the circuit is
So, the phase angle difference between the current and voltage at the resonance is 0 degrees
The voltage drop across the resistor is given by
Note: According to the guidelines, only one question can be answered. I have answered two questions. please post the remaining two questions separately.
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