Presentation ONGrowth of Current in R-L and Growth of Charge in R-C Series Circuit

Name : Muhammad Awais razaClass : Msc 3rd Roll No: 3414ME

|||

CENTRE FOR HIGH ENERGY PHYSICSUniversity of the Punjab

Growth of Current in R-L Series Circuit

R-L Series CircuitWhen an inductor having inductance “L” and resistor having resistance “R” is connected in series, the circuit is called R-L series circuit.

Introduction

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

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.

Apply Kirchhoff's voltage law in the above series RL circuit,

Rearranging the above equation,

||||||||||||||

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.

“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

Growth of Charge in R-C series Circuit

IntroductionR-C Series CircuitWhen a Capacitor having capacitance “C” Resistor having resistance “R “ connected in series circuit , the circuit is called R-C series circuit.

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

Apply Kirchhoff's voltage law in the above series R-C circuit,

V- IR- Vc = 0As, I= dq/ dt and Vc =q/ t

Rearranging get

|||||||||||||

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

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%

Screen-Print OF Simulation

Thanks for Listening & Watching