---
title: "Current and frequency in series RLC"
subject: "Basic Electrical Engineering"
chapter: 6
key: "semester_1/basic_electrical_engineering:rlc-series-current-frequency-relationship"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/rlc-series-current-frequency-relationship
site: BCT Engineering
---

# Current and frequency in series RLC

Basic Electrical Engineering · Chapter 6: Single-phase AC Circuits

- Asked in: 2067 Asoj, 4 marks
- Video: [Series RLC Circuits, Resonant Frequency, Inductive Reactance & Capacitive Reactance - AC Circuits](https://www.youtube.com/watch?v=2GvqQvohP2k) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/rlc-series-current-frequency-relationship
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-6

## Question

Describe briefly: Current and supply frequency relationship of a RLC series circuit

## Short answer

Current is minimum at low and high frequencies, peaking at resonant frequency f₀ where X_L=X_C, impedance Z=R (minimum). Below f₀ circuit capacitive, current leads; above, inductive, current lags. The bell-shaped curve’s sharpness depends on R.

## Answer

In a series RLC circuit the impedance is

Z = √(R² + (ωL − 1/ωC)²), and the current is I = V/Z.

Because X_L = ωL rises with frequency and X_C = 1/(ωC) falls with it, the current changes with frequency as follows.

- **Low frequency (f < f₀):** X_C is large and X_C > X_L. The circuit is capacitive, Z is large and the current is small. The current leads the voltage.
- **At resonance (f = f₀):** X_L = X_C, so they cancel. Z = R (minimum) and the current is maximum, I₀ = V/R, in phase with the voltage (unity power factor).

  f₀ = 1/(2π√(LC))
- **High frequency (f > f₀):** X_L > X_C. The circuit is inductive, Z increases and the current falls. The current lags the voltage.

```text
   I
   │              I0 = V/R
   │               _.-._
   │             /       \
   │            /         \
   │          /             \
   │  ___..-'                 '-..___
   └────────────────┴───────────────────── f
                    f0
```

The curve is bell-shaped (a resonance curve). A small R gives a tall, narrow (sharp) peak and a high quality factor Q = ω₀L/R. A large R gives a flatter, wider peak. The bandwidth is BW = f₂ − f₁ = f₀/Q, measured between the half-power points where I = I₀/√2.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Series RLC impedance is:
   A. √(R^2 + ωL^2)
   B. Z = √(R^2 + (ωL − 1/ωC)^2)
   C. R
   D. R + ωL + 1/ωC
   Answer: B. Inductive and capacitive reactances oppose. (Key point: Impedance)

2. At resonance:
   A. I zero
   B. Z maximum
   C. X_L = X_C, Z = R minimum, I maximum = V/R, pf unity
   D. X_L = 0
   Answer: C. f0 = 1/(2π√(LC)). (Key point: Resonance)

3. For f < f0, the circuit is:
   A. Inductive, lagging
   B. Capacitive, with current leading the voltage
   C. Resistive
   D. Open circuit
   Answer: B. X_C is large at low frequency and exceeds X_L. (Key point: Below resonance)

4. A small R gives:
   A. Lower resonant frequency
   B. No peak
   C. Tall, narrow peak with high Q
   D. Flat, wide peak
   Answer: C. Q = ω0L/R; bandwidth = f0/Q. (Key point: Effect of R)

## Related in Basic Electrical Engineering

- [Series RLC circuit analysis](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aseries-rlc-100-0-12h-28-27uf) — Basic Electrical Engineering, chapter 6
- [Parallel RLC supply current](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aparallel-r-l-c-200v-supply-current) — Basic Electrical Engineering, chapter 6
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- [Series-parallel AC circuit analysis](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aseries-parallel-ac-r1-15-l1-0-05-200v) — Basic Electrical Engineering, chapter 6, asked 2×
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## Related in other subjects

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- [RLC circuit current](https://www.bctengineer.com/question.md?key=semester_1%2Fmathematics_i%3Aapp-rlc-circuit-current) — Mathematics I, chapter 4
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- [Series RLC resonance: f0, bandwidth, half power, Q](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Aseries-resonance-derive-f0-bw-q) — Electrical Circuit Theory, chapter 1