Testing and Application of
various Capacitor Circuits
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Faculty: B. Allen
Capacitive reactance
Capacitive Reactance XC – Measured in
ohms, it is the ability of a capacitor to oppose
current flow without the dissipation of energy.
XC = 1/(2πfC)
f = frequency in hertz
C = Capacitance in farads
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Purely resistive circuit
In a purely resistive circuit, there is a 0° phase shift between
current and voltage. Current is in phase with voltage.
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Purely capacitive circuit
In a purely capacitive circuit, there is a 90° phase shift
between current and voltage. Current leads voltage by 90°.
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RC series circuit
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Vector diagram
An arrangement of vectors showing the phase relationships
between two or more ac quantities of the same frequency.
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Voltage in an RC series circuit
VS = V + V
2
R
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2
C
Impedance in an RC series
circuit
Impedance (Z) – Measured in ohms, it is the total
opposition a circuit offers to current flow (resistive
and reactive).
Z= R +X
2
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2
C
V
I=
Z
V
Z=
I
V = I×R
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Phase angle or phase shift
XC
θ = arctan
R
VC
θ = arctan
VR
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Power in a purely resistive
circuit
P =V ×I
2
V
P=
R
2
P = I ×R
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Power in a purely resistive
circuit
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Power in a purely capacitive
circuit
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Power in an RC Circuit
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Power factor
Resistive Power or True Power (PR) – The
average power consumed by a circuit during a
complete cycle of alternating current.
PR = I × R
2
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Reactive power or
imaginary power
Also called wattless power, it is the power value obtained by
multiplying the effective value of current by the effective
value of voltage and the sine of the angular phase difference
between current and voltage.
PX = V × I sin θ
PX = I × X C
2
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Apparent Power
The power value obtained in an ac circuit by
multiplying the effective values of voltage and
current, which reach their peaks at different
times.
PA = P + P
2
R
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2
X
Power Factor
The ratio of actual power to apparent power. A pure resistor
has a power factor of 1 or 100% while a capacitor has a power
factor of 0 or 0%.
PF =
True
Apparent
PF = cosθ
(PR )
Power (PA )
Power
R
PF =
Z
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Voltage in a parallel RC circuit
VR = VC = VS
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Current in a parallel RC circuit
VS
IR =
R
VS
IC =
XC
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IT = I + I
2
R
2
C
Phase angle in a parallel RC
circuit
IC
θ = arctan
IR
R
θ = arctan
XC
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Impedance in a parallel RC
circuit
VS
Z=
IT
Z=
R× XC
R +X
2
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2
C
Power in a parallel RC circuit
PR = I × R
PX = I × X C
2
R
2
C
PA = P + P
2
R
2
x
PR
PF =
PX
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Testing a capacitor using an
ohmmeter
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Capacitance meter
An instrument used to measure the capacitance of a capacitor
or a circuit.
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Combining ac and dc
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Capacitive voltage divider
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RC filters
Filter – A network composed of resistors, capacitors, and
inductors used to pass certain frequencies yet block others
through heavy attenuation.
Low-Pass Filter – A network or circuit designed to pass any
frequencies below a critical or cutoff frequency and reject or
heavily attenuate all frequencies above.
Attenuate – To reduce in amplitude an action or a signal.
High-Pass Filter – A network or circuit designed to pass any
frequencies above a critical or cutoff frequency and reject or
heavily attenuate all frequencies below.
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Frequency response curve
A graph indicating how effective a circuit or device
responds to the frequency spectrum.
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Low-pass filter
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High-pass filter
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RC Integrator
Integrator – A device that approximates, and whose output is
proportional to, an integral of the input signal.
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RC Differentiator
Differentiator – A circuit whose output voltage is proportional
to the rate of change of the input voltage. The output
waveform is then the time derivative of the input waveform,
and the phase of the output waveform leads that of the input
by 90°.
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End of
Testing and Application of
various Capacitor Circuits
Online Resource for ETCH 213
Faculty: B. Allen