Electrical Energy

For a Point Charge

$$ \large W = \Delta U = q \Delta V \quad \left(= \frac{1}{2} m v^2 \right) $$

Thus,

$$ \large \Rightarrow \quad v = \sqrt{\frac{2qV}{m}} $$

Power

$$ \large P = I^2 R = IV = \frac{V^2}{R} \quad (\because V = IR) $$

Energy in a Capacitor

$$ \large U = \frac{1}{2} CV^2 $$

Energy in a Inductor

$$ \large U = \frac{1}{2} L I^2 $$

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