The document discusses the behavior of an RLC circuit when a DC voltage is applied. It first defines the basic components of a resistor, capacitor, and inductor. It then measures the voltage across each component when different resistor, capacitor and inductor values are used in the RLC circuit. The voltage across the resistor drops exponentially as the capacitor charges. The capacitor takes more time to charge as its capacitance increases. The inductor opposes current changes, causing the voltage across it to slow the rate of current change initially and become zero once the current stabilizes. Larger inductor values result in more time needed to store energy and more oscillations in the circuit.

2. BEHAVIOR OF RLC CIRCUIT IN DC
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3. IN THE PRESENTATION
• Basic concepts about Resistor, Capacitor and Inductor.
• Oscilloscope
• Multiplexer
• Voltage across Resistor.
• Voltage across Capacitor
• Voltage across Inductor.

4. RESISTOR
• A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit
element.
• Resistors act to reduce current flow, and, at the same time, act to lower voltage levels within circuits.
• The electrical function of a resistor is specified by its resistance.

5. CAPACITOR
• A capacitor is a passive two-terminal electrical component used to store electrical energy temporarily in
an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical
conductors (plates) separated by a dielectric.
• When there is a potential difference across the conductors an electric field develops across the dielectric,
causing positive charge +Q to collect on one plate and negative charge −Q to collect on the other plate. If
a battery has been attached to a capacitor for a sufficient amount of time, no current can flow through the
capacitor. However, if a time-varying voltage is applied across the leads of the capacitor, a displacement
current can flow.

6. INDUCTOR
• An inductor, also called a coil is a passive two-terminal electrical component which resists changes
in electric current passing through it.
• It consists of a conductor such as a wire, usually wound into a coil.
• When a current flows through it, energy is stored temporarily in a magnetic field in the coil.
• When the current flowing through an inductor changes, the time-varying magnetic field induces
a voltage in the conductor, according to Faraday’s law of electromagnetic induction, According to Lenz's
law the direction of induced e.m.f is always such that it opposes the change in current that created it. As a
result, inductors always oppose a change in current.

7. OSCILLOSCOPE
• An oscilloscope is a laboratory instrument commonly used to display and analyze the waveform of
electronic signals.
• Oscilloscope can display alternating current (AC) or pulsating direct current (DC) waveforms having a
frequency as low as approximately 1 hertz (Hz) or as high as several megahertz (MHz).
• Time is displayed from left to right on the horizontal scale. Instantaneous voltage appears on the vertical
scale, with positive values going upward and negative values going downward.

8. MULTIPLEXER
• Multiplexer (mux) is a device that selects one of several analog or digital input signals and forwards the
selected input into a single line.
• Multiplexers are mainly used to increase the amount of data that can be sent over the network within a
certain amount of time and bandwidth.

9.  RLC circuit consists of resistor, inductor, and a capacitor.
Resistor, Inductor and Capacitor are connected in series with
each other. There is supply given to the circuit which will be
DC and we have to analyze the response of the circuit.

10. VOLTAGE ACROSS RESISTOR
• We will give DC supply to the RLC circuit.
• We will use an Oscilloscope, a Multiplexer and Transfer function.
• We will assign the values for Resistance, Capacitance and Inductance.
• As we are keen to know about the Voltage across Resistor so we simply put Inductance and Capacitance
constant.
• In first Transfer Function Resistance is taken as 1 ohm, Capacitance as 1 Farad and Inductance as 1 Henry.
• In second Transfer Function Resistance is taken as 5 ohm, Capacitance as 1 Farad and Inductance as 1
Henry.
• In third Transfer Function Resistance is taken as 10 ohm, Capacitance as 1 Farad and Inductance as 1 Henry.

13. • When the switch is first closed all the voltage is across resistor. As the charges
starts to flow across capacitor the voltage across the resistor drops exponentially.
This is because capacitor has a voltage drop and circuit conforms the KVL. After
some time voltage across resistor becomes zero because capacitor is fully
charged.
• As we increase the value of resistor so the voltage across it will increase and the
same phenomenon charging of capacitor.
• As resistance is further increased the voltage across it will increase in initial time
when the switch is closed.

14. VOLTAGE ACROSS CAPACITOR

16. • As the capacitor is initially uncharged so when it is connected with the supply
then its plates begins to charge up. When it becomes fully charged the electric
field between the plates cancels the effect of the electric field generated by the
battery, and there is no further movement of charge.
• As capacitance increases it will take more time to charge.
• As Capacitance is further increased so the time required to charge that capacitor
will increase.

17. VOLTAGE ACROSS INDUCTOR

19. • When we close the switch, the sudden increase of the current produces self emf
that will oppose the current change. This self emf is opposite of voltage across
inductor. As we know that inductance store energy in DC so the voltage across
inductor will slow down the current change and this will make voltage across
inductor smaller. When the current becomes stable, the inductor creates no more
opposition and VL becomes zero. This is basically the storage phase.
• As Inductance increase so this will take more time to store energy in Inductor.
There will be oscillations due to increase in Inductance.
• As Inductance is increased further it will take more time to store the energy and
the oscillations will increase as well.