Practice problems

Capacitor practice problems

A capacitor stores charge on two plates, Q = C × V, and energy with it. These ten problems start with reading the value printed on a part and work up to picking a capacitor for a set energy and finding the energy it gives out. Type your answer to check it, and open the working whenever you want it.

The method

Q = C × V

C = Q over V when you want the capacitance
E = ½ × C × V² for the energy it stores, in joules
C = 2 × E over V² to pick a capacitor for an energy
In parallel, capacitances add. In series they combine like resistors in parallel: C₁ × C₂ over C₁ + C₂ for two

Turn µF, nF and pF into farads before you multiply: 470 µF = 0.00047 F. Then Q comes out in coulombs and E in joules. 1 µF = 1000 nF, and 1 nF = 1000 pF.

The problems

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

Problem 1 of 10
A capacitor is marked 0.047 µF. What's that in nanofarads?
Show the working
1. 1 µF = 1000 nF, so multiply by 1000.
2. 0.047 µF × 1000 = 47 nF
Answer: 47 nF
Problem 2 of 10
A small ceramic capacitor is marked 4700 pF. What's that in nanofarads?
Show the working
1. 1 nF = 1000 pF, so divide by 1000.
2. 4700 pF ÷ 1000 = 4.7 nF
Answer: 4.7 nF
Problem 3 of 10
A 470 µF capacitor is charged to 5 V. How much charge sits on each plate, in millicoulombs?
Show the working
1. Use Q = C × V, with C in farads: 470 µF = 0.00047 F.
2. Q = 0.00047 F × 5 V = 0.00235 C
3. 0.00235 C is 2.35 mC: +2.35 mC on one plate and −2.35 mC on the other.
Answer: 2.35 mC
Problem 4 of 10
A capacitor holds 66 µC on each plate when it's charged to 3 V. What is its capacitance?
Show the working
1. Turn Q = C × V round: C = Q over V.
2. C = 66 µC over 3 V = 22 µF. Microcoulombs per volt give microfarads.
Answer: 22 µF
Problem 5 of 10
100 µF, 47 µF and 22 µF capacitors are wired in parallel. What's the total capacitance?
Show the working
1. In parallel the plates join up into bigger plates, so the capacitances add.
2. C = 100 + 47 + 22 = 169 µF
Answer: 169 µF
Problem 6 of 10
A 220 µF capacitor is charged to 9 V. How much energy does it store, in millijoules?
Show the working
1. Use E = ½ × C × V², with C = 220 µF = 0.00022 F.
2. E = ½ × 0.00022 F × (9 V)² = ½ × 0.00022 × 81 = 0.00891 J
3. 0.00891 J is 8.91 mJ.
Answer: 8.91 mJ
Problem 7 of 10
A capacitor stores 12 mJ when it's charged to 6 V. How much energy does it store at 12 V?
Show the working
1. The capacitance doesn't change, and energy goes with V². Twice the voltage gives 2² = 4 times the energy.
2. 4 × 12 mJ = 48 mJ
Answer: 48 mJ
Problem 8 of 10
A 10 µF and a 15 µF capacitor are wired in series. What's the total capacitance?
Show the working
1. Capacitors in series combine the way resistors in parallel do: the product over the sum, for two.
2. C = 10 × 15 over 10 + 15 = 150 over 25 = 6 µF, less than the smaller one.
Answer: 6 µF
Problem 9 of 10
You need a capacitor that stores 45 mJ at 15 V. What capacitance does that take, in microfarads?
Show the working
1. Turn the energy formula round: C = 2 × E over V², with E = 45 mJ = 0.045 J.
2. C = 2 × 0.045 over 15² = 0.09 over 225 = 0.0004 F
3. 0.0004 F is 400 µF. That isn't an E6 value, so pick 470 µF, the next one up.
Answer: 400 µF
Problem 10 of 10
A 2200 µF capacitor charged to 10 V discharges until it's down to 5 V. How much energy has it given out, in millijoules?
Show the working
1. At 10 V: E = ½ × 0.0022 F × (10 V)² = 0.11 J = 110 mJ.
2. At 5 V: E = ½ × 0.0022 F × (5 V)² = 0.0275 J = 27.5 mJ.
3. It gave out 110 − 27.5 = 82.5 mJ: three quarters of its energy, though its voltage only halved.
Answer: 82.5 mJ

Build it in a free lesson

“Capacitors” is lesson 1 of 5 in Capacitor Caves, Electronics World 3. Free with an account. Lessons unlock in order, so you’ll do the 15 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

“Capacitors” is lesson 1 of 5 in Capacitor Caves, Electronics World 3. Free with an account. Lessons unlock in order, so you’ll do the 15 before it first.

Or start from the very first lesson, no account needed

Check it with a calculator

Capacitor energy calculatorJoules and charge in a capacitor, and how much your circuit can use.

The ideas behind it

Questions people ask

What do µF, nF and pF mean?

They're millionths, billionths and trillionths of a farad. 1 µF = 1000 nF and 1 nF = 1000 pF, so 0.1 µF, 100 nF and 100,000 pF are the same part. Turn any of them into farads before you use Q = C × V or E = ½ × C × V².

Do capacitors in parallel add up like resistors in series?

Yes. In parallel the plates join into bigger plates, so the capacitances add: 47 µF beside 47 µF is 94 µF. In series they combine the way resistors in parallel do, so the total is smaller than either one.

Why does twice the voltage store four times the energy?

At twice the voltage, a capacitor holds twice the charge, and every bit of that charge is pushed in at twice the voltage. Two times two is four, which is the V² in E = ½ × C × V².