Useful for R-L and R-C series Circuit means and definition

2. Presentation
ON
Growth of Current in R-L and Growth of Charge
in R-C Series Circuit
Name : Muhammad Awais raza
Class : Msc 3rd
Roll No: 3414ME
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CENTRE FOR HIGH ENERGY PHYSICS
University of the Punjab

3. Growth of Current in R-L Series Circuit
R-L Series Circuit
When an inductor having inductance “L” and resistor having resistance “R” is connected in series, the
circuit is called R-L series circuit.
Introduction

4. Consider a simple R-L circuit in which resistor, R and inductor, L are connected in series
with a voltage supply of V volts. Let us think the current flowing in the circuit is I (amp) and
current through resistor and inductor is IR and IL respectively. Since both resistance and
inductor are connected in series, so the current in both the elements and the circuit remains
the same. i.e IR = IL =I. Let VR and VL be the voltage drop across resistor and inductor.
Applying Kirchhoff voltage law ( i.e sum of voltage drop must be equal to apply voltage) to
this circuit we get,
Explanation

5. Consider an inductor and a resistor is connected in series along with battery of
voltage V as shown in figure. Initially the switch is open. Let us say at time 't' we
close the switch and the current ‘i' starts flowing in the circuit but it does not
attains its maximum value rapidly due to the presence of inductor in the circuit
as we know inductor has a property to oppose the change in the current
flowing through it.

6. Apply Kirchhoff's voltage law in the above series RL circuit,
Rearranging the above equation,
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Exact Solution Numarical Solution
Using Euler’s Method
I ( t+dt )=(( V- I(t) ×R ) / L ) × dt+ I(t)
Graph shown in above figure I vs t
Integrate
Get solution finally
We can easily find Growth of current using this
expression.

7. “The Time at which the value of growing Current in circuit becomes 63% of
maximum current is called inductive time constant”
The term L/R in the equation is called the Time Constant, ( τ ) of the
RL series circuit, get by using V=IR and V=LI/t relation and it is
defined as time taken by the current to reach its maximum steady
state value and the term V/R represents the final steady state value of
current in the circuit.
Inductive Time Constant

8. Growth of Charge in R-C series Circuit
Introduction
R-C Series Circuit
When a Capacitor having capacitance “C” Resistor having resistance “R “ connected in series
circuit , the circuit is called R-C series circuit.

9. Explanation
Consider a circuit containing a capacitor of capacitance C and a resistor R connected
to a constant source of emf (battery) through a key (K) as shown below in the figure8:
q(t)
t

10. Apply Kirchhoff's voltage law in the above series R-C circuit,
V- IR- Vc = 0
As, I= dq/ dt and Vc =q/ t
Rearranging get
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Exact Solution Numerical Solution
Using Euler’s MethodIntegrate t=0 to t=t get
q = q0 (1-Exp^(-t/RC)) q( t+ dt)=((V×C-q)/ R×C)× dt + q(t)
The graph q vs t Shown in above figure
We can easily find the Growth of charge
in circuit

11. Capacitive Time Constant
“The time at which the charge on Capacitor has increased by 63%
of its maximum value is called capacitive time constant”
The quantity RC has the dimension of time. It can be proved by
using V=IR and q=CV relation. This time is denoted by tL .
63%

12. Screen-Print OF Simulation

13. Thanks
for
Listening & Watching