1. DIFFERENTIAL EQUATION AND LINEAR ALGEBRA
• RLC CIRCUIT ,PENDULUM
• Prsented by-NIRMALYA SWAIN-220301120177
2. CONTENT
• Introduction of the topic(RLC CIRCUIT)
• Dreivation and example (RLC CIRCUIT
• Pndulum
• Conclusion
3. RLC CIRCUIT
• An RLC circuit is an electrical circuit
consisting of a resistor (R), an
inductor (L), and a capacitor (C),
connected in series or in parallel.
The name of the circuit is derived
from the letters that are used to
denote the constituent components
of this circuit, where the sequence
of the components
may vary from RLC.
4. DERIVATION OF RLC CIRCUIT
• RLC circuits have many applications as oscillator circuits. Radio receivers and television sets
use them for tuning to select a narrow frequency range from ambient radio waves. In this role,
the circuit is often referred to as a tuned circuit. An RLC circuit can be used as a band-pass
filter, band-stop filter, low-pass filter or high-pass filter. The tuning application, for instance, is an
example of band-pass filtering. The RLC filter is described as a second-order circuit, meaning
that any voltage or current in the circuit can be described by a second-order differential
equation in circuit analysis.The three circuit elements, R, L and C, can be combined in a
number of different topologies. All three elements in series or all three elements in parallel are
the simplest in concept and the most straightforward to analyse. There are, however, other
arrangements, some with practical importance in real circuits. One issue often encountered is
the need to take into account inductor resistance. Inductors are typically constructed from coils
of wire, the resistance of which is not usually desirable, but it often has a significant
effect on the circuit.
• RLC circuit used in Voltage magnification
5. EXAMPLE OF RLC CIRCUIT----
•For Example-AM/FM radios with analog tuners typically
use an RLC circuit to tune a radio frequency. Most
commonly a variable capacitor is attached to the tuning
knob, which allows you to change the value of C in the
circuit and tune to stations on different frequencies.
6. • XL=2πfL=2×3.14×100×0.02
• XC=1/2πfC=1/2×π×100×5×10−6
• And similarly, conductance is
• G=1/R=1/50
• Y= √ G2+(BL−BC)2
• Z=1/Y=1/79.5
• The power factor of the circuit is
• cosθ=G/Y=20/79.5
• Where the angle between current and voltage
• θ=cos−1 0.25
• IR=V/R=50/50=1Amp
• Where the source current is the vector combination of
all these individual currents
• Is= √ I2R+(IL−IC)2
• Is= √ 1+(3.9−0.16)2
7. PENDULUM
Oscillation denotes the cyclic transformation between two forms of energy. Let's have
a closer look at the processes of a mechanical system.
IN THIS Figure ::An iron sphere with the mass m is hanging on a thin cord of length l.
Position (2) is the equilibrium position of the arrangement. Now the sphere is pulled
back at an angle α. Thereby the sphere is lifted to the height h, leading to a potential
energy.
EPot = m * g * h
8. CONCLUSION
• The resistor, inductor, and capacitor are connected in parallel across an ac
source.
• Voltage is common in all components and is taken as a reference for the phasor
diagram.
• Impedances of RLC parallel circuit, the addition of admittances.
• Source current is the vector summation of individual currents.
