RL and RC Circuits

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R-L and R-C Circuits

• EE341 Energy Conversion
• Ali Keyhani
• Circuit Theory
• Lecture 1

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R-L Circuit

Considering a R-L circuit
If at t0, the switch is closed. What will be the
response inductor current i?
The system differential equation is
3
R-L Circuit
After some time (transient state), the current
reaches steady state as shown in the figure.
Voltage source
Steady state
Transient state
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R-L Circuit
At steady state, v and i can be represented by
phasor V and I, where
?V is the phase angle of V. ?I is the phase
angle of I. It is determined by ?V and impedance
angle ? (?I ?V - ? )
or
The differential equation becomes
5
R-L Circuit

Let
Inductor Reactance
Let
We have
Generally we choose V as reference, then ?V 0
I lags V
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R-L Circuit

The power supplied by the power source is
Lagging positive reactive power
Or in other form,
7
R-C Circuit

Considering a R-C circuit

_
If at t0, the switch is closed. What will be the
response capacitor voltage vc?
The system differential equation is
8
R-C Circuit
After some time (transient state), the voltage
reaches steady state as shown in the figure.
Voltage source
Steady state
Transient state
9
R-C Circuit

At steady state, v and vc can be represented by
phasor V and VC, where
or
10
R-C Circuit

so
Let
Capacitor Reactance
Let
We have
Generally we choose V as reference, then ?V 0
I leads V
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R-C Circuit

The power supplied by the power source is
Leading negative reactive power
Or in other form,