APPLICATION OF DIFFERENTIAL EQUATION TO R-L CIRCUIT

1. Subject: Engineering Mathematics III
Topic: Application of Differential Equation to
R-L Circuit
Guided by:
Ms. Chaitali Wadaskar
Group No : 06
(SCOB48) Uttam Singh

2. Introduction to D.E
 A differential equation is a mathematical equation that relates some
function with its derivatives.
 Differential equations first came into existence with the invention
of calculus by Newton and Leibniz.
 Ordinary Differential Equation an ordinary differential equation(ODE) is
a differential equation containing one or more functions of one
independent variable and its derivatives.
 Partial differential equation (PDE) is a differential equation that
contains unknown multivariable functions and their partial derivatives.
 Linear Differential Equation contains differential
coefficient and dependent variable in the first
degree and they are not multiplied together.

3. Applications of Differential Equations
 To Calculate the Exponential decay of Radioactive material in
Nuclear Physics.
 To Calculate the heat equation in thermodynamics
 Laplace's equation, which defines harmonic functions
 In Electrodynamics to Calculate the Resistance,
Inductance, Capacitance in Various circuits.
 Newton's law of cooling in thermodynamics.

4. D.E in Resistor-Inductor (RL) Circuit
 The RL circuit shown above has a resistor and an inductor connected in
series. A constant voltage V is applied when the switch is closed.
 The (variable) voltage across the resistor is given by:

5.  The (variable) voltage across the inductor is given by:
 Kirchhoff's voltage law says that the directed sum of the voltages around a
circuit must be zero. This results in the following differential equation:
 The solution of the differential equation is: