Check the dimensional correctness of E = ½CV²
Energy stored in a capacitor. The energy held by a capacitor charged to a potential V.
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
E = (1/2) C V2E[M L2 T-2]=1/2 C V2[M L2 T-2]Step by step
1. What each symbol stands for
- E energy [M L2 T-2]
- C capacitance [M-1 L-2 T4 A2]
- V electric potential [M L2 T-3 A-1]
2. The dimensions of each term
- E [M L2 T-2] [M L2 T-2]
- 1/2 C V2 1/2 × [M-1 L-2 T4 A2] × [M L2 T-3 A-1]2 [M L2 T-2]
3. Compare
Every term has dimensions [M L2 T-2], so the equation is dimensionally consistent.
What it proves and what it does not
It can show
- Every term that is added or subtracted has the same dimensions, so the sum makes sense.
- Both sides of the equals sign have the same dimensions.
- Angles inside sin, cos and similar functions are pure numbers.
It cannot show
- A pure number such as 1/2 or 2π has no dimensions, so a check cannot see a missing or wrong one.
- Two quantities with the same dimensions, such as work and torque, cannot be told apart.
- A sign error or a wrong power that keeps the dimensions equal goes unnoticed.
Matching dimensions are necessary but not sufficient. Pure numbers such as 1/2 or 2π have no dimensions, so a check cannot see them, and an equation with matching dimensions can still be wrong.
Look up each quantity
E = ½CV²: quick answers
Is E = ½CV² dimensionally correct?
Yes. Every term has the same dimensions, [M L² T⁻²], so E = ½CV² is dimensionally consistent. That does not prove the equation itself is correct.
Does a dimension check prove E = ½CV² is right?
No. A check can show that an equation is wrong, but it cannot show that it is right. Pure numbers such as 1/2 and 2π have no dimensions, so the check cannot see them.