Physics - Recall for Chapter 21; Capacitance

What is capacitance?

The charge stored per unit potential difference.

What happens to the two plates of an uncharged capacitor when a p.d. is applied across it?

Charge flows off of one plate and flows onto the other, causing one to become positive and one to become negative.

What is the Farad?

\[CV^{-1},\ \text{Coulombs per Volt}\]

How do you calculate the total capacitance $C _ T$ for capacitors $C _ 1, C _ 2, C _ 3$ in parallel?

\[C_T = C_1 + C_2 + C_3\]

How do you calculate the total capacitance $C _ T$ for capacitors $C _ 1, C _ 2,\ \ldots$ in series?

\[\frac{1}{C_T} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}\]

If capacitors are connected in series, what quantity is the same for all the capacitors?

Charge stored.

If capacitors are connected in parallel, what quantity is the same for all capacitors?

Potential difference.

What is represented by the gradient of a charge-pd graph for a capacitor?

Capacitance.

What is represented by the area under a charge-pd graph for a capacitor?

Energy stored.

What is the relationship between energy stored $E$ and potential difference $V$ for a capacitor?

\[E \propto V^2\]

What is the relationship between energy stored $E$ and the charge on a capacitor $Q$?

\[E = Q^2\]

Out of $Q, V, I$, which variables follow the relationship $x = x_0 e^{-t/CR} when discharging a capacitor?

All of them, $Q, V, I$

Out of $Q, V, I$, which variables follow the relationship $x = x_0 e^{-t/CR} when charging a capacitor?

\[Q, V\]

How do you calculate the time constant in a capacitor circuit?

\[CR\]

What is meant by the constant-ratio nature of exponential decay?

In equal time intervals, the quantity decreases by equal factors.

How much charge remains after a duration of one time constant when discharging a capacitor?

\[e^{-1} \approx 0.37\]

How much charge remains after a duration of $N$ time constants when discharging a capacitor?

\[e^{-N}\]

What is represented by the gradient of a charge-time graph when charging a capacitor?

The current.

Can you give two uses of a capacitor?

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