**Title : LC Oscillator and Damped
Oscillation**

**Apparatus
:**

** ****Science Workshop Interface 750**** **
**1**

** ****Voltage sensor
** **(
PASCO CI-6503
) **
**2**

**Capacitors **(
)

**Inductors ( 240-turn coil with two soft-iron C-cores, one
soft iron C-core )**

**Objective
:**

**1. Study the
oscillation of voltage when a charged capacitor is
connected **

** across an
inductor.**

**2. Determine
the phase relationship between , the
voltage **

** across capacitor and
inductor. **

**Theory
: **

Put** **

which is simple harmonic oscillation with the period T.

**The
following diagram shows eight stages in a cycle of oscillation of an LC
circuit. The bar graph below the figure shows the stored electric and
magnetic potential**

**The total energy U present at any instant in an oscillating LC
circuit is given by**

**If we assume the circuit resistance to be zero, there is no
energy transfer to Joule heat and U remains constant with time. This leads
to**

**where
U is a constant and
**

**Now. Q and I are not independent variables, being related
by **

**Differentiating yields **

**Substituting these two expressions into Eq. (2) leads
to **

**This equation is mathematically of exactly the same form as
equation of motion of mass-spring system,
**

**L C Circuit Analogy to Simple Harmonic Motion as shown in
the following table**

**Mechanical
Damped Harmonic Motion**

**The simple harmonic motion relates to the motion of a body
acted on by a special kind of force and in friction-free
conditions. The amplitude of SHM is a constant. If the
amplitude of the oscillation gradually decreases to zero as a result of
friction, the motion is said to be damped harmonic
motion. The magnitude of the frictional force usually
depends on the speed.**

**Electromagnetic Damped Oscillation**

**The resistance in the LC circuit will dissipate the energy. The
variation of voltage across the capacitor is shown in the following
figure.**

**Using a square wave**

**Apply a square wave to the LC-series combination, at each
rising edge of the square wave, the capacitor would be charged. Since the
charging current also passes through the inductor, oscillation would
occur. At the falling edge, the charged capacitor would be discharged
through the inductor. Again, oscillation would occur. **

**
In the following figure, the first diagram represents the variation of
voltage across the capacitor and the second diagram represents the
variation of voltage across the inductor.**

**Procedure
:**

**Hardware setup :**

**1. Connect
the Interface to the Computer, turn on the interface, and turn on
the computer.**

**2. Connect the
Voltage Sensor to the interface**

**3. Connect the
function generator ( OUTPUT ports on the interface ) directly across
the LC **

**
circuit ****and voltage sensor from analog channel A across
the inductor and voltage sensor **

**
****from
analog ****channel B across the capacitor as shown in the
following diagram.**

Use the "Output" feature of the interface to supply a voltage to the inductor - capacitor circuit.

Use the Voltage Sensors to measure the voltage across the capacitor and inductor

**4. The signal generator
is set to output a 5 volt, "positive only" square wave at **

** 10
Hz.**

The Signal Generator is set to ' Auto' so it will start and stop automatically.

**For
a given 240-turn air core coil, the variation of voltage across capacitor
and inductor were measured.**

**The
experiment was repeated with different
combination of capacitances ( )
and inductances ( a 240 turns coil with one soft-iron core and a 240 turns
coil with two soft-iron C-cores ). **

**Data Analysis
:**

**Relationship
between the period of LC Oscillation and the LC value**

**Variation
of the period of LC Damped Oscillation**

**How does the amplitude of an LC damped oscillation
vary with time
?**

**Phase
relationship between the voltage across capacitor and
inductor**

**Discussion :**

1. What are the precautions of this experiment ?

2. Design an experiment to investigate how the current fluctuates

after connecting the charged capacitor across the inductor.

3. Discuss the application of LC circuit in our daily life.

** **