Question

When a generator, resistor, inductor, and capacitor are wired in series, they form a

driven oscillator. There is a resonant frequency for every oscillator; if it is driven at the

resonant frequency,

a) what will happen to the amplitude of the current?

b) what will happen to the amplitude of the voltage across the resistor?

c) what will happen to the amplitude of the voltage across the inductor and

capacitor combined?

2. If the oscillator is driven at a frequency that is NOT the resonant frequency,

a) what will happen to the amplitude of the current?

b) what will happen to the amplitude of the voltage across the resistor?

c) what will happen to the amplitude of the voltage across the inductor and

capacitor combined?

Answer 1

Solution) when resistor , inductor and capacitor are connected in series to a generator , then same current flows through the circuit .

We have

V = iZ

Here i is current

Z is impedance

V is source voltage

Z = (R^2 + (XL - Xc)^2)^(1/2)

Here R is resistance

XL is reactance of inductor

Xc is reactance of capacitance

At resonant frequency , XL = Xc

Z = R

So at resonance impedance (Z) decreases

(a) Amplitude of current(i) increases as impedance (Z) decreases from relation V = iZ

i = V/Z

So current is inversely proportional to impedance as impedance decreases current increases .

(b) Voltage across resistor VR = (i)R

As current(i) increases voltage across resistor increases .

(c) voltage across inductor and capacitor combined ,

V' = i(XL - Xc)

Here also voltage across inductor and capacitor combined increases as current increases .

(2) if it is not driven at a frequency but not resonant resonant frequency then impedance Z

Z = (R^2 + (XL - Xc)^2)^(1/2)

XL = 2(pi)fL

Xc = 1/(2(pi)fC)

So here impedance increases .

(a) Amplitude of current decreases as impedance increases .

i = V/Z

(b) Voltage across resistor decreases as current decreases .

VR = (i)R

(c) voltage across inductor and capacitor combined decreases as current decreases .

V' = i(XL - Xc)