Unit 23
Resistive-Capacitive Parallel
Circuits
Unit 23
Resistive-Capacitive Parallel Circuits
Unit 23
Resistive-Capacitive Parallel Circuits
• The current through the resistance will be
in phase.
• The current through the capacitor will
phase shift 90°.
• The total current will have a phase shift
between 0 and 90°.
Unit 23
Resistive-Capacitive Parallel Circuits
Objectives:
• Discuss characteristics of R-C parallel
circuits.
• Discuss all R-C parallel circuit values.
• Discuss the circuit impedance.
• Discuss the apparent power, power vectors,
and power factor.
Unit 23
Resistive-Capacitive Parallel Circuits
Phase relationship of current.
Unit 23
Resistive-Capacitive Parallel Circuits
When resistance (R) and capacitance (C)
are connected in parallel, the voltage
across all the devices will be in phase and
will have the same value (Kirchhoff’s law).
R-C parallel circuit.
Unit 23
Resistive-Capacitive Parallel Circuits
Circuit Values
• IR = current flow through the resistor
• P = watts (true power)
• IC = current flow through the capacitor
• VARs = volt-amperes-reactive (reactive
power)
• C = capacitance of the capacitor (farads)
• IT = total circuit current
Unit 23
Resistive-Capacitive Parallel Circuits
Unit 23
Resistive-Capacitive Parallel Circuits
Total Current
• The total current is the vector sum of the
currents in the parallel branches.
• IT = √IR2 + IC2
Unit 23
Resistive-Capacitive Parallel Circuits
Circuit Values
• Z = total impedance of the circuit
• VA = volt-amperes (apparent power)
• PF = power factor
  θ = degrees of phase shift (theta)
Current vectors.
Unit 23
Resistive-Capacitive Parallel Circuits
Unit 23
Resistive-Capacitive Parallel Circuits
Impedance
• Circuit impedance (Z) is the total circuit
opposition to the flow of electricity.
• Z = E / IT (Ohm’s law)
• Z = 1 / √ (1/R)2 + (1/XC)2
Phase relationship.
• Z = R x XC / √R2 +XC2
Unit 23
Resistive-Capacitive Parallel Circuits
Unit 23
Resistive-Capacitive Parallel Circuits
Apparent Power
• Apparent power is the product of the
applied voltage and the total current and is
measured in volt-amperes.
• VA = E x IT (Ohm’s law)
• Vector addition of reactive power and true
power also yields apparent power.
• VA = √ Watts2 + VARs2
Example Circuit #1
• A resistance of 30Ω is connected in
parallel with a capacitive reactance of
20Ω. The circuit is connected to a 240
VAC power source with a frequency of 60
Hz.
• R = 30Ω, XC = 20Ω
• E = 240 V @ 60 Hz
Unit 23
Resistive-Capacitive Parallel Circuits
Unit 23
Resistive-Capacitive Parallel Circuits
Power vectors.
Example circuit #1 values.
Unit 23
Resistive-Capacitive Parallel Circuits
•
•
•
•
Power Factor
Power factor (PF) is the ratio of true power
to apparent power.
PF = P / VA (Ohm’s law)
The cosine of angle theta is equal to the
power factor.
PF = cosine θ
Unit 23
Resistive-Capacitive Parallel Circuits
Example circuit #2.
Unit 23
Resistive-Capacitive Parallel Circuits
Example circuit #2 values.
Unit 23
Resistive-Capacitive Parallel Circuits
Review:
1. Current flow in the resistive part of a
parallel R-C circuit is in phase with the
voltage.
2. Current flow in the capacitive part of an
R-C circuit leads the voltage by 90°.
3. The voltage is the same across any leg of
a parallel circuit.
Unit 23
Resistive-Capacitive Parallel Circuits
Review:
4. The amount the current and voltage are
out of phase with each other is determined
by the ratio of resistance to capacitance.
5. The circuit power factor is the ratio of true
power to apparent power.