ELE1110C Tutorial 2

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ELE1110C Tutorial 2

• 20-9-2006
• Luk Chun Pong

Outline -Basic concepts of Capacitors -RC
circuits (DC) -Examples
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Capacitor

• -Store energy in the electric field

• Q CV
• Q Total Charge
• C Capacitance
• V Voltage across the capacitor
• C actually depends on the
• permittivity of the dielectric,
• the area of the plates and
• the spacing between them.

dielectric
conducting plates
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Important Laws

• Capacitor in parallel
• C C1 C2
• Capacitor in series
• Proof?
• In series, current passes through the capacitors
  is the same
• In parallel, voltage across the capacitor is the
  same

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Important Laws (3)

• Rate of change of voltage across the capacitor
  the current pass through the capacitor

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Time domain description (case 1)

• dV/dt I/C Constant

Current Source (I is constant)
Slope dV/dt
dV
dt
I and C are constants
Not common!
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Time domain description (case 2)

• Constant voltage source

Voltage across the capacitor at time t
Current at time t
Remember this is a DC circuit
Initial Condition, t 0 Vc 0
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Solving the differential equation
First order differential equation
Separable Differential Equations, integrate both
sides
Dont forget the Constant k
Substitute using the initial conditions
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General formula for charging and discharging a
capacitor
Charging
R
V0
Discharging
Vc
C
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Charging and discharging
Charging
Vc(t)
Discharging
t
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RC circuit Time constant

• RC Resistance of the resistor x Capacitance
  of the capacitor
• How long does it take to charge up/discharge the
  capacitor
• The unit of RC is second
• t RC, 63
• t 5RC, 99

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Question

• Find out the time needed for
• Vc 0.5 V0?
• Vc V0?

DC RC circuit

• Transient state Solving differential equations
• Steady state Open circuit

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Problem sheet 2 Q2

• In the following circuit, prove that the energy
  required to charge the capacitor from 0 to V0
  volt is 0.5CV02. What is the energy dissipated in
  discharging the capacitor from V to 0 volt?
  Remember this result - the energy dissipated DOES
  NOT depend on the resistor R!

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Charging
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Discharging
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Another Example

• Consider the following RC circuit

X
The circuit has been operated at the above state
for a long time. At t 0, the switch move to X,
find v at t 1s
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Solution

• For t lt 0, v 15V
• So, v(0) 15V

Using the general formula, V0 30, Vc(0) 15, t
1, CR 2s Vc(1) 20.9V