The energy stored equals the area under a Q-V graph, which is a straight line through the
Capacitors - OCR A-Level Physics
- The energyThe capacity to do work. Measured in joules (J). stored equals the area under a Q-V graph, which is a straight line through the origin (since $Q = CV$).
- There are three equivalent expressions, each useful depending on what quantities you are given.
$$\begin{aligned}
E &= \frac{1}{2}QV \\
&= \frac{1}{2}CV^2 \\
&= \frac{Q^{2}}{2C}
\end{aligned}$$
Examiner Tips and Tricks
- In 'show that' questions on energyThe capacity to do work. Measured in joules (J). stored, start from E = area under Q-V graph = $\frac{1}{2}$QV, then substitute Q = CV or V = Q/C to derive the other two forms.
- Examiners want to see the substitution step.
Common Mistake
MEDIUM
Wrong: Using $E = QV$ for the energyThe capacity to do work. Measured in joules (J). stored in a capacitor.
Right: $E = \frac{1}{2}QV$. The factor of $\frac{1}{2}$ arises because the p.d. builds up from 0 to V as chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). is added. QV would be the energy if all chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). were added at full voltageThe energy transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference..
Right: $E = \frac{1}{2}QV$. The factor of $\frac{1}{2}$ arises because the p.d. builds up from 0 to V as chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). is added. QV would be the energy if all chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). were added at full voltageThe energy transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). Informal term for potential difference..