Introduction to Series Circuits

In a series circuit, all components are connected end-to-end, forming a single path for current flow. The total impedance in a series circuit is the sum of individual impedances contributed by resistors, inductors, and capacitors.

R-L Series Circuit

An R-L series circuit consists of a resistor (R) and an inductor (L) connected in series.

Key Characteristics:

• The resistor contributes to real power dissipation.
• The inductor stores energy in its magnetic field, introducing a phase difference.
• The current lags behind the voltage by an angle φ, where tan(φ) = XL/R.

Impedance (Z):

Z = √(R2 + XL2), where XL = ωL is the inductive reactance.

Voltage and Current Relationship:

• Voltage across the resistor: VR = I × R.
• Voltage across the inductor: VL = I × XL.

Phasor Diagram:

The voltage phasor is the vector sum of VR and VL.

R-C Series Circuit

An R-C series circuit contains a resistor (R) and a capacitor (C).

Key Characteristics:

• The resistor dissipates power.
• The capacitor stores energy in its electric field and introduces a phase shift.
• The current leads the voltage by an angle φ, where tan(φ) = XC/R.

Impedance (Z):

Z = √(R2 + XC2), where XC = 1/(ωC) is the capacitive reactance.

Voltage and Current Relationship:

• Voltage across the resistor: VR = I × R.
• Voltage across the capacitor: VC = I × XC.

Phasor Diagram:

The voltage phasor is the vector sum of VR and VC.

R-L-C Series Circuit

An R-L-C series circuit contains a resistor (R), inductor (L), and capacitor (C).

Key Characteristics:

• The resistor dissipates energy.
• The inductor and capacitor exchange energy.
• The total impedance determines whether the circuit is inductive, capacitive, or at resonance.

Impedance (Z):

Z = √(R2 + (XL - XC)2), where XL = ωL and XC = 1/(ωC).

Resonance:

• Resonance occurs when XL = XC, minimizing impedance to Z = R.
• At resonance, the circuit achieves maximum current.

Voltage and Current Relationship:

Voltage across components depends on their reactances and resistance. Current phase depends on the net reactance.

Phasor Diagram:

Phasors of VR, VL, and VC combine to show total voltage.

Applications of Series Circuits

• R-L Circuits: Used in motors, transformers, and inductive loads.
• R-C Circuits: Found in electronic filters and timing circuits.
• R-L-C Circuits: Used in tuning circuits, radios, and oscillators.

Problem-Solving Techniques

• Use Ohms Law for individual components: V = IZ.
• Apply Kirchhoff Voltage Law (KVL) to analyze the total voltage.
• Draw phasor diagrams to visualize phase relationships.
• Calculate total impedance and phase angle for current.

Conclusion

This lesson explored the behavior of R-L, R-C, and R-L-C series circuits in AC systems. It covered impedance, phase relationships, and practical problem-solving techniques. In the next lesson, we will study resonance in series circuits.