“Capacitors do it backwards”
Series and parallel
Resistors add in series; capacitors add in parallel. Whenever you are unsure, remember they are the opposite of resistors.
Class 12 Physics · Gujarat Board, CBSE, GUJCET, JEE and NEET
Capacitance formulas
Capacitance is where circuit questions begin. Only four ideas are needed: how capacitance is defined, what a dielectric does, how capacitors combine, and how much energy is stored. Series and parallel behave opposite to resistors, and that swap is where marks are lost.
14 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
Capacitance
| What | Formula | Symbols and notes |
|---|---|---|
| Definition | C = Q/V | unit farad; one farad is very large |
| Parallel plate capacitor | C = ε₀A/d | A plate area, d separation |
| With a dielectric | C = Kε₀A/d | K is the dielectric constant, always greater than 1 |
| Spherical capacitor, isolated sphere | C = 4πε₀R | capacitance of a sphere of radius R |
Combinations
| What | Formula | Symbols and notes |
|---|---|---|
| In series | 1/C = 1/C₁ + 1/C₂ + … | charge is the same on each, total C is smaller than the smallest |
| In parallel | C = C₁ + C₂ + … | voltage is the same across each, capacitances add |
| Two capacitors in series | C = C₁C₂/(C₁ + C₂) | the product over sum shortcut |
Energy
| What | Formula | Symbols and notes |
|---|---|---|
| Energy stored | U = ½CV² = ½QV = Q²/2C | three forms of one result |
| Energy density | u = ½ε₀E² | energy per unit volume of the field |
| Loss on connecting two capacitors | ΔU = C₁C₂(V₁ − V₂)²/2(C₁ + C₂) | energy is always lost, as heat and radiation |
| Common potential | V = (C₁V₁ + C₂V₂)/(C₁ + C₂) | after the two are joined |
Dielectrics
| What | Formula | Symbols and notes |
|---|---|---|
| Battery still connected | V constant, C rises, Q rises, U rises | the battery supplies the extra charge |
| Battery disconnected | Q constant, C rises, V falls, U falls | the field pulls the slab in |
| Field inside the dielectric | E = E₀/K | the induced charges oppose the original field |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“Connected or cut, ask first”
Dielectric questions
With the battery still connected the voltage is fixed. With it disconnected the charge is fixed. Decide which is constant before writing anything else.
“Half CV squared”
Energy stored
U = ½CV². The half is there because the capacitor charges up gradually, so the average voltage is half the final one.
Where marks go
The mistakes that cost the most.
- Adding capacitors in series the way resistors add in series. In series it is the reciprocals that add.
- Forgetting to decide whether the battery stays connected. Every dielectric numerical turns on that one question.
- Using U = QV without the half. The half comes from the charging being gradual.
- Thinking charge is shared equally between series capacitors of different values. In series the charge is the same on each, and it is the voltages that differ.
- Assuming energy is conserved when two charged capacitors are connected. Some is always lost.
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