Series Parallel Circuit Calculator
Calculate equivalent values for series and parallel circuits with R, C, L, and mixed RLC components.
Need quick resistor-only calculations? Try our dedicated Series/Parallel Resistor Calculator.
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Formulas
R series: Req = R1 + R2 + ... + Rn
Difference from Series/Parallel Resistor Calculator
The Series/Parallel Resistor Calculator handles DC resistor-only circuits with a simple interface. This calculator expands to capacitors, inductors, and mixed RLC circuits with AC impedance analysis, resonant frequency, and quality factor calculations.
Understanding Series & Parallel Circuits
Series and parallel circuits are the two fundamental ways to connect electrical components. In a series circuit, components are connected end-to-end so the same current flows through each. In a parallel circuit, components share the same voltage across their terminals. Understanding equivalent values—total resistance, capacitance, or inductance—is essential for circuit design and analysis. For AC circuits with mixed RLC components, impedance replaces simple resistance, incorporating both magnitude and phase angle to fully describe the circuit's opposition to current flow.
Formulas
How to Calculate Series & Parallel Circuits
Frequently Asked Questions
Why do capacitors behave opposite to resistors in series/parallel?
Resistors oppose current flow, so adding them in series increases total opposition (they add). Capacitors store charge, and adding them in series reduces total capacitance because the plate area effectively stays the same while the gap increases. In parallel, capacitors add (more plate area), while resistors in parallel reduce total resistance (more paths for current). This is because capacitance relates to geometry (area/gap), while resistance relates to obstruction of current.
What is the resonant frequency of an RLC circuit?
The resonant frequency fr is the frequency at which the inductive reactance XL equals the capacitive reactance XC, causing them to cancel out. At resonance, the circuit behaves as if only the resistor is present. The formula is fr = 1 / (2π√(LC)). For a series RLC circuit, impedance is minimized at resonance; for a parallel RLC circuit, impedance is maximized.
What is the quality factor Q in an RLC circuit?
The quality factor Q measures the sharpness of resonance. A higher Q means a narrower bandwidth and more selective frequency response. For a series RLC circuit, Q = (1/R)√(L/C) = XL/R at resonance. Q also equals the ratio of stored energy to energy dissipated per cycle. Typical values range from less than 1 (damped) to over 100 (highly resonant).
How do I calculate impedance in an AC circuit?
Impedance Z is the total opposition to AC current, combining resistance R and reactance X. For a series RLC circuit: Z = √(R² + (XL − XC)²), where XL = 2πfL and XC = 1/(2πfC). The phase angle φ = arctan((XL − XC) / R) indicates whether the circuit is inductive (positive) or capacitive (negative).
When should I use this calculator vs. the Series/Parallel Resistor Calculator?
Use the Series/Parallel Resistor Calculator when working with DC circuits containing only resistors—it offers a streamlined interface for quick resistor calculations. Use this calculator when your circuit includes capacitors, inductors, or mixed RLC components, or when you need AC impedance analysis, resonant frequency, or quality factor calculations that go beyond simple DC resistance.