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(a)
The frequency of the RC circuit.
(a)
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Answer to Problem 46P
The frequency of the series RC circuit is
Explanation of Solution
The resistor with resistance of
Write the expression for voltage drop across the resistor
Here,
Write the expression for voltage drop across the capacitor
Here,
Write the expression for capacitive reactance
Here,
Substitute (III) in (II)
Equate (I) and (IV) since resistor and capacitor has the same rms voltage
Rearrange for
Substitute
Thus, the frequency of the series RC circuit is
(b)
The rms voltage of the resistor and capacitor as fraction of the source voltage.
(b)
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Answer to Problem 46P
The rms voltage of the resistor and capacitor as fraction of the source voltage is
Explanation of Solution
The phasor diagram for the series RC circuit is given below:
Write the expression for source voltage using the phasor diagram
Here,
Substitute
Rearrange
Take square root on both sides
Since both resistor and capacitor has the same rms voltage.
Thus, the rms voltage of resistor and capacitor is not half the rms voltage of the source.
(c)
The phase angle between the source voltage and the current.
(c)
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Answer to Problem 46P
The phase angle between the voltage and current is
Explanation of Solution
Write the expression for phase angle
Here,
Rearrange
Write the expression for impedance
Substitute
Multiply both numerator and denominator by
Substitute (I) and (II) in (XIV).
Substitute (VII) in (XV).
Substitute (IX) in (XV).
Thus, the phase angle between the voltage and current is
(d)
The impedance of the series RC circuit.
(d)
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Answer to Problem 46P
The impedance is
Explanation of Solution
Rearrange (XI)
Substitute
Thus, the impedance is
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