Unit 22
Resistive-Capacitive Series
Circuits
Unit 22
Resistive-Capacitive Series Circuits
Unit 22
Resistive-Capacitive Series Circuits
• VARsC = volt-amperes-reactive (reactive
power)
• VA = volt-amperes (apparent power)
• PF = power factor
 θ = angle theta ( the angle the voltage
and current are out of phase with each
other)
Unit 22
Resistive-Capacitive Series Circuits
Objectives:
• Discuss the relationship of resistance (R)
and capacitance (C) in an R-C series
circuit.
• Calculate all circuit values in an R-C series
circuit.
• Discuss power factors and angle theta in an
R-C series circuit.
Unit 22
Resistive-Capacitive Series Circuits
Impedance (Z)
• Total circuit impedance is the vector
addition of resistance (R) and capacitive
reactance (XC).
• Z = √R2 + XC2
Unit 22
Resistive-Capacitive Series Circuits
• Z = total circuit impedance
• I = total circuit current
• ER = voltage drop across the resistor
• P = watts (true power)
• C = capacitance
• EC = voltage drop across the capacitor
Vector addition of impedance.
Unit 22
Resistive-Capacitive Series Circuits
Unit 22
Resistive-Capacitive Series Circuits
Total Current (I)
• Total circuit current is equal to the applied
voltage divided by the impedance.
• IT = E / Z
Unit 22
Resistive-Capacitive Series Circuits
Capacitance and Capacitive Reactance
• Capacitance (C) = 1 / (2fXC)
• Capacitive reactance (XC)
Unit 22
Resistive-Capacitive Series Circuits
Voltage Drop across the Resistor
• In a series circuit, the current is the same
in all parts of the circuit. Therefore, all the
current flows through the resistor. This
results in a measurable voltage drop
across the resistor (Ohm’s law).
• ER = I x R
Vector addition of voltage drops.
Unit 22
Resistive-Capacitive Series Circuits
Unit 22
Resistive-Capacitive Series Circuits
Voltage Drop across the Capacitor
• In a series circuit, the current is the same
in all parts of the circuit. Therefore, all the
current flows through the capacitor. This
results in a measurable voltage drop
across the capacitor (Ohm’s law).
• E C = I x XC
True Power
• True power (P) is measured in watts and
is produced by only the resistor (Ohm’s
law).
• P = ER x I
Unit 22
Resistive-Capacitive Series Circuits
Reactive Power
• Reactive power (VARsC) is the product of
the capacitor volt drop times the current.
• VARsC = EC x I
Unit 22
Resistive-Capacitive Series Circuits
Unit 22
Resistive-Capacitive Series Circuits
Angle Theta
• Angle theta is the number of degrees that
the voltage and current are out of phase.
• cosine (PF)-1 = θ
• Try using the inverse or second function
on your calculator to convert between the
power factor and theta.
Unit 22
Resistive-Capacitive Series Circuits
Apparent Power
• Apparent power (VA) is the product of the
applied voltage times the current.
• VA = ET x I
• Vector addition and the Pythagorean
theorem allow the use of another formula.
• VA = √P2 + VARsC2
Angle theta is the degrees of separation.
Unit 22
Resistive-Capacitive Series Circuits
Unit 22
Resistive-Capacitive Series Circuits
Power Factor
• Power factor (PF) is a ratio of the true
power to the apparent power.
• PF = P / VA or PF = Watts / VA
• PF = cosine θ
Example circuit with values.
Unit 22
Resistive-Capacitive Series Circuits
Review:
1. The amount of phase angle difference
between voltage and current in an R-C
series circuit is the ratio of resistance to
capacitance.
2. True power is only produced by resistive
parts.
Unit 22
Resistive-Capacitive Series Circuits
Review:
3. Power factor is the ratio of true power to
apparent power.
4. In a series circuit, the current is the same
through all the components. Therefore,
the voltage drops across the resistive
and capacitive parts become out of
phase with each other.