METERS
Capacitance ($C$)1.0 C₀
Charge ($Q$)1.0 Q₀
Voltage ($V$)1.0 V₀
Stored Energy ($U$)1.0 U₀
E-Field ($E$)1.0 E₀
■ Dielectric Mechanics:
Inserting a dielectric always increases $C$. The way other variables react depends strictly on the system state.
■ Connected to Battery (V constant)
$V$ is held constant. Vì $C$ goes up, $Q=CV$ dictates that $Q$ increases. Energy $U = \frac{1}{2}CV^2$ increases. The battery intrinsically does work to pump more charge.
■ Isolated System (Q constant)
$Q$ is trapped on the plates. Since $C$ goes up, $V = Q/C$ dictates that $V$ drops. Because the dielectric molecules align and cancel out some $E$-field, the total Field $E$ drops. Energy $U = \frac{Q^2}{2C}$ also decreases (the dielectric is physically sucked in!).
Inserting a dielectric always increases $C$. The way other variables react depends strictly on the system state.
■ Connected to Battery (V constant)
$V$ is held constant. Vì $C$ goes up, $Q=CV$ dictates that $Q$ increases. Energy $U = \frac{1}{2}CV^2$ increases. The battery intrinsically does work to pump more charge.
■ Isolated System (Q constant)
$Q$ is trapped on the plates. Since $C$ goes up, $V = Q/C$ dictates that $V$ drops. Because the dielectric molecules align and cancel out some $E$-field, the total Field $E$ drops. Energy $U = \frac{Q^2}{2C}$ also decreases (the dielectric is physically sucked in!).