Practice problems

Capacitive and inductive reactance practice problems

Reactance is how much a capacitor or a coil opposes AC, in ohms, and it depends on the frequency. These ten problems start with a single reactance and work up to the current through a resistor and capacitor in series. Type your answer to check it, and open the working whenever you want it.

The method

X_C = 12π f C

X_L = 2π f L

A capacitor's reactance falls as frequency rises: ten times the frequency, a tenth of the reactance
A coil's reactance rises with frequency, in step with it
I = V over X: Ohm's law with reactance, peak with peak or RMS with RMS
|Z| = √(R² + X²) for a resistor and a reactance in series

Use hertz, farads and henries. The working keeps π at full precision and rounds only the answer, to 3 significant figures.

The problems

Type your answer and tap Check. Every one has the working, step by step.

Problem 1 of 10
What is the reactance of a 10 µF capacitor at 50 Hz?
Show the working
1. Use X_C = 1 over 2π f C, with C = 10 µF = 0.00001 F.
2. 2π × 50 × 0.00001 ≈ 0.003142, so X_C = 1 over 0.003142 ≈ 318 Ω
Answer: 318 Ω
Problem 2 of 10
What is the reactance of a 47 mH coil at 1 kHz?
Show the working
1. Use X_L = 2π f L, with f = 1000 Hz and L = 47 mH = 0.047 H.
2. X_L = 2π × 1000 × 0.047 ≈ 295 Ω
Answer: 295 Ω
Problem 3 of 10
A capacitor has a reactance of 800 Ω at 200 Hz. What is its reactance at 2 kHz?
Show the working
1. Frequency is on the bottom of X_C = 1 over 2π f C, so ten times the frequency gives a tenth of the reactance.
2. X_C = 800 Ω over 10 = 80 Ω
Answer: 80 Ω
Problem 4 of 10
A coil has a reactance of 50 Ω at 400 Hz. What is its reactance at 1.2 kHz?
Show the working
1. Frequency is on top of X_L = 2π f L, so the reactance rises in step with it. 1.2 kHz is three times 400 Hz.
2. X_L = 3 × 50 Ω = 150 Ω
Answer: 150 Ω
Problem 5 of 10
What is the reactance of a 220 nF capacitor at 5 kHz?
Show the working
1. C = 220 nF = 220 × 10⁻⁹ F, and f = 5000 Hz.
2. 2π × 5000 × 220 × 10⁻⁹ ≈ 0.006912, so X_C = 1 over 0.006912 ≈ 145 Ω
Answer: 145 Ω
Problem 6 of 10
At what frequency does a 47 nF capacitor have a reactance of 2.2 kΩ? Give it in kilohertz.
Show the working
1. Swap f and X_C in the formula: f = 1 over 2π X_C C.
2. f = 1 over 2π × 2200 × 47 × 10⁻⁹ = 1 over 0.0006497 ≈ 1539 Hz ≈ 1.54 kHz
Answer: 1.54 kHz
Problem 7 of 10
What inductance has a reactance of 1 kΩ at 10 kHz? Give it in millihenries.
Show the working
1. Turn X_L = 2π f L round: L = X_L over 2π f.
2. L = 1000 over 2π × 10,000 ≈ 0.0159 H = 15.9 mH
Answer: 15.9 mH
Problem 8 of 10
5 V RMS at 1 kHz sits across a 2.2 µF capacitor. What RMS current flows, in milliamps?
Show the working
1. First the reactance: X_C = 1 over 2π × 1000 × 0.0000022 ≈ 72.34 Ω.
2. Then Ohm's law with X: I = V over X_C = 5 V over 72.34 Ω ≈ 0.0691 A = 69.1 mA RMS
Answer: 69.1 mA
Problem 9 of 10
A 500 Ω resistor is in series with a capacitor whose reactance is 1.2 kΩ. What is the circuit's impedance, in kilohms?
Show the working
1. R and X are 90° apart, so they combine like the sides of a right-angled triangle: |Z| = √(R² + X²).
2. |Z| = √(0.5² + 1.2²) = √(0.25 + 1.44) = √1.69 = 1.3 kΩ, not the 1.7 kΩ you'd get by adding them.
Answer: 1.3 kΩ
Problem 10 of 10
10 V peak at 1 kHz drives a 1 kΩ resistor in series with a 220 nF capacitor. What peak current flows, in milliamps?
Show the working
1. The capacitor's reactance: X_C = 1 over 2π × 1000 × 220 × 10⁻⁹ ≈ 723 Ω.
2. The impedance: |Z| = √(1000² + 723²) ≈ 1234 Ω.
3. I = 10 V over 1234 Ω ≈ 0.0081 A = 8.1 mA peak
Answer: 8.1 mA

Build it in a free lesson

“Reactance” is lesson 2 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 22 before it first.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“Reactance” is lesson 2 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 22 before it first.

Or start from the very first lesson, no account needed

Check it with a calculator

Capacitive and inductive reactance calculatorA capacitor's or a coil's ohms at any frequency, the current, and the impedance with R.

The ideas behind it

Questions people ask

Is reactance the same thing as resistance?

Both are in ohms, and both go into Ohm's law: I = V ÷ X. But reactance changes with frequency, and an ideal capacitor or coil takes no average power. Energy flows in for a quarter of a cycle and back out the next, where a resistor turns it all into heat.

Why does a capacitor's reactance fall as the frequency rises?

A faster wave changes its voltage faster, and a capacitor's current depends on how fast its voltage changes. So the same voltage drives more current, which is a smaller reactance. A coil is the other way round: it fights changes in current, so it pushes back harder at high frequencies.

Why can't I just add R and X?

Their voltages peak a quarter of a cycle (90°) apart, so they never reach their peaks together. They add like the sides of a right-angled triangle: |Z| = √(R² + X²). 3 kΩ and 4 kΩ make 5 kΩ, not 7 kΩ.