# Lab Report

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• Topic: Inductor, RL circuit, Capacitor
• Pages : 13 (2870 words )
• Published : May 5, 2013

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A. ENG237-02: Transients in RC and RL Circuits

0. Introduction
The objective of this experiment is to study the DC transient behaviors of RC and RL circuits.

This experiment has divided into 6 parts:
1. Charging curve from measured data ( R = 10M Ω and C = 4 mF ) 2. Draw the charging curve by the graphical method
3. Discharging curve from measured data ( R = 5M Ω and C = 4 mF ) 4. Draw the discharging curve by the graphical method
5. Display of the charging and discharging curve of capacitor 6. Display of the charging and discharging curve of inductor

1. Theories
(a) Capacitor
Capacitor is an electrical passive device for storing charge in the form of electric field. In its simplest from, It consists basically consists of two conductors which are separated by a dielectric medium (non-conductor) such as air, waxed paper, plastics, etc. The capacitance of capacitor is directly proportional to the surface areas and the inverse of the separation of the two conductors. The dielectric constant of the non-conductor is also affecting the capacitance.

FIGURE 1 Capacitor symbol

For an ideal capacitor, the capacitor current iC is proportional to the time rate of change of the voltage across the capacitor:

Where C is the proportionality constant and is known as capacitance.

(b) Inductor
Inductor is an electrical passive device for storing energy in the form of magnetic field. In its simplest from, It consists basically consists of a wire loop or coil. The inductance is directly proportional to the number of turns in the coil. Inductance also depends on the radius of the coil and on the type of material around which the coil is wound.

FIGURE 2 Inductor symbol

For an ideal inductor, the inductor voltage VL is proportional to the time rate of change of the current through the inductor:

Where L is the proportionality constant and is known as inductance.

(c) RC circuit
RC circuit is consists of resistor and capacitor. The simplest form is shown in below.

FIGURE 3 Simplest RC circuit

For discharging case, when t<0 , then VS=0
By Kirchhoff’s Voltage Law, at the steady state,
0=VC-VR
0=IR-QC
Assume the resistor and the capacitor are ideal (i.e. R and C are constant). Then we have
0=-RdQdt-QC (I=-dQdt) dQdt=-QRC
QoQ1QdQ=0t-1RCdt
lnQQo=-tRC,
Q=Qoe-tRC
By VC=QC ,
VC=QoCe-tRC
VC=Voe-tτ
Where time constant, τ=RC For half life,
Vo2=Voe-t12τ
t12=ln2×τ=0.693τ
When t=τ,
VC=Voe-1
VC=0.368Vo
From the above, the half-life of capacitor voltage was related to the time constant τ , when the time equal to t = 0.693τ , then the voltage remains half. And if the time equal to time constant, the capacitor voltage would decrease to 0.368Vo For charging case, when t<0 , then VS=VO

By Kirchhoff’s Voltage Law, at the steady state,
0=VC-VR
0=IR-QC
Assume the resistor and the capacitor are ideal (i.e. R and C are constant). Then we have
0=-RdQdt-QC (I=-dQdt) dQdt=-QRC
QoQ-Qo1QdQ=0t-1RCdt
lnQ-QoQo=-tRC
Q=Qo(1-e-tRC)
By VC=QC ,
VC=QoC(1-e-tRC)
VC=Vo(1-e-tτ)
Where time constant, τ=RC For half life,
Vo2=Vo(1-e-t12τ)
t12=ln2×τ=0.693τ
When t=τ,
VC=Vo(1-e-1)
VC=0.632Vo
From the above, the half-life of capacitor voltage was related to the time constant τ , when the time equal to t = 0.693τ , then the voltage remains half. And if the time equal to time constant, the capacitor voltage would decrease to 0.632Vo

(d) RL circuit
RL circuit is consists of resistor and inductor. The simplest form is shown in...