Capacitance Problems- Practice Exercises with Solutions

Capacitance Problems: What You Actually Need to Master

Capacitance shows up everywhere in circuits. Power supplies, filters, timing circuits, energy storage—everything. If you cannot solve basic capacitance problems, you will hit a wall fast in electronics and physics classes.

This guide cuts through the theory. You get practice problems with worked solutions, the formulas you actually need, and zero motivational garbage.

Quick Refresher: The Core Formulas

Before diving into problems, lock these equations into your brain:

• C = Q/V — Capacitance equals charge divided by voltage
• Q = CV — Charge on a capacitor
• W = ½CV² — Energy stored in a capacitor
• C = ε₀εᵣA/d — Capacitance of a parallel plate capacitor
• τ = RC — Time constant for RC circuits

If these look unfamiliar, memorize them first. Problems will not make sense without them.

Series vs. Parallel Capacitors

Students consistently mess this up. Here is the difference:

Capacitors in Parallel

Voltage is the same across each capacitor. Total capacitance adds up.

C_total = C₁ + C₂ + C₃ + ...

Think of it like expanding the plate area. More area means more capacitance.

Capacitors in Series

Charge is the same on each capacitor. Total capacitance decreases.

1/C_total = 1/C₁ + 1/C₂ + 1/C₃ + ...

Think of it like increasing the plate separation. More distance means less capacitance.

Practice Problem 1: Basic Capacitance Calculation

Problem: A capacitor stores 0.004 coulombs of charge when connected to a 200V battery. What is its capacitance?

Given:

• Q = 0.004 C
• V = 200 V

Solution:

Use C = Q/V

C = 0.004 / 200

C = 20 μF (microfarads)

Practice Problem 2: Energy Stored in a Capacitor

Problem: A 100 μF capacitor is charged to 50V. Calculate the energy stored.

Given:

• C = 100 μF = 100 × 10⁻⁶ F
• V = 50V

Solution:

Use W = ½CV²

W = ½ × (100 × 10⁻⁶) × (50)²

W = ½ × 100 × 10⁻⁶ × 2500

W = 0.125 joules

Answer: 0.125 J

Practice Problem 3: Series Capacitors

Problem: A 4 μF capacitor is connected in series with a 6 μF capacitor. Find the total capacitance.

Solution:

For series: 1/C_total = 1/C₁ + 1/C₂

1/C_total = 1/4 + 1/6

1/C_total = 3/12 + 2/12 = 5/12

C_total = 12/5 = 2.4 μF

Notice the total is smaller than either individual capacitor. This trips people up every time.

Practice Problem 4: Parallel Capacitors

Problem: A 3 μF capacitor, a 5 μF capacitor, and a 7 μF capacitor are connected in parallel across a 12V source. Find the total capacitance and total charge stored.

Solution:

Step 1: Total Capacitance

C_total = 3 + 5 + 7 = 15 μF

Step 2: Total Charge

Q_total = C_total × V

Q_total = 15 × 10⁻⁶ × 12

Q_total = 180 μC

Practice Problem 5: RC Time Constant

Problem: A 50 kΩ resistor is connected in series with a 200 μF capacitor. How long does it take to charge to 63.2% of the supply voltage?

Solution:

The time constant τ = RC

τ = 50,000 × 200 × 10⁻⁶

τ = 10 seconds

At one time constant, a capacitor charges to 63.2% of the supply voltage. So the answer is 10 seconds.

Practice Problem 6: Parallel Plate Capacitor

Problem: A parallel plate capacitor has plate area of 0.01 m² and plate separation of 0.001 m. The dielectric constant is 4.5. Calculate the capacitance. (ε₀ = 8.85 × 10⁻¹² F/m)

Solution:

Use C = ε₀εᵣA/d

C = (8.85 × 10⁻¹²) × 4.5 × (0.01 / 0.001)

C = 8.85 × 10⁻¹² × 4.5 × 10

C = 8.85 × 10⁻¹² × 45

C = 398.25 pF (picofarads)

Capacitor Combinations: Quick Comparison

Do not memorize this table. Understand it. Once you grasp why charge stays equal in series and voltage stays equal in parallel, you will not forget.

Common Mistakes to Avoid

• Adding capacitances in series. They do not add—they reciprocate. Students lose points on this constantly.
• Confusing units. Convert everything to farads, volts, and coulombs before calculating. Mixing μF and pF will wreck your answer.
• Forgetting the energy formula is ½CV², not CV². The half matters.
• Using the wrong formula for RC time constant. τ = RC works for charging and discharging. Some people try to use V = IR. Wrong.

How to Solve Any Capacitance Problem

Follow this process every time:

1. Identify what is given. Write down Q, V, C, or whatever values the problem provides.
2. Identify what is asked. Charge? Capacitance? Energy? Time constant?
3. Pick the right formula. Match what you need to what you have.
4. Convert units. Everything to base units before calculating.
5. Plug in and solve. Show your work. Partial credit exists for a reason.
6. Check your answer. Does the magnitude make sense? Is a 5000F capacitor realistic? Probably not.

Final Word

Capacitance problems are straightforward once you know the formulas and understand series versus parallel behavior. Practice the six problems above until you can solve them without looking at the solutions. That is the real test.