Capacitor charge and discharge (A-level only) Flashcards – AQA A-level Physics (7408)

Why does the current decrease as a capacitor charges through a resistor from a constant-voltage supply?

As the capacitor voltage rises, the voltage across the resistor falls, so the current decreases towards zero.

What is the charge $Q$ at time $t$ for an initially uncharged capacitor charging through a resistor?

$Q=Q_\infty\left(1-\mathrm{e}^{-t/(RC)}\right)$

What is the capacitor voltage $V$ at time $t$ for an initially uncharged capacitor charging through a resistor?

$V=V_\infty\left(1-\mathrm{e}^{-t/(RC)}\right)$

What is the current $I$ at time $t$ for an initially uncharged capacitor charging through a resistor, in terms of the initial current $I_0$?

$I=I_0\mathrm{e}^{-t/(RC)}$

What is the initial current when an uncharged capacitor charges through resistance $R$ from a constant-voltage supply $V_\infty$?

$I_0=\frac{V_\infty}{R}$

What shapes do the charge–time and capacitor-voltage–time graphs have during charging?

Both rise steeply at first, then approach their final values asymptotically.

What shape does the current–time graph have while a capacitor charges through a resistor?

It starts at its maximum and falls asymptotically towards zero.

Why does the current decrease as a capacitor discharges through a resistor?

The capacitor loses charge, so its potential difference falls, reducing the current.

For a capacitor discharging through a fixed resistor, how does charge $Q$ depend on time?

$Q=Q_0\mathrm{e}^{-t/(RC)}$

For a capacitor discharging through a fixed resistor, how does its voltage $V$ depend on time?

$V=V_0\mathrm{e}^{-t/(RC)}$

For a capacitor discharging through a fixed resistor, how does the current magnitude $I$ depend on time?

$I=I_0\mathrm{e}^{-t/(RC)}$

For a capacitor discharging through a resistor, what is the initial current magnitude in terms of initial voltage $V_0$ and resistance $R$?

$I_0=\frac{V_0}{R}$

How does the direction of discharge current compare with charging current under the same sign convention?

It is in the opposite direction.

What is the shape of a graph of charge, voltage or discharge-current magnitude against time?

It falls steeply at first, then approaches zero asymptotically.

What can a signed discharge-current graph look like when discharge current is negative?

It lies below the time axis and approaches zero from below.

What does the gradient of a charge–time graph give?

The signed current: $I=\frac{\mathrm{d}Q}{\mathrm{d}t}$

For a capacitor of constant capacitance, how are charge and voltage related?

$Q=CV$

For a capacitor of constant capacitance, what does the gradient of its voltage–time graph give?

$\frac{\mathrm{d}V}{\mathrm{d}t}=\frac{I}{C}$

For a given capacitor of constant capacitance, what does a steeper charge–time or voltage–time graph indicate about the current?

A greater current magnitude.

What does the signed area under a current–time graph over an interval give?

The change in charge: $\Delta Q=\int I\,\mathrm{d}t$ Area below the time axis contributes a negative change.

Does the area under a voltage–time or charge–time graph directly give the change in capacitor charge?

No. The quantities and units on the axes determine what the area represents.

What is the time constant of an RC circuit, and what is its unit?

$\tau = RC$, measured in seconds.

How does increasing resistance or capacitance affect the rate of change in an RC circuit?

It increases the time constant, slowing the change.

How can the RC time constant be found from a graph of exponentially decaying charge, voltage or current magnitude?

Find the elapsed time for the quantity to fall to about 37% ($\mathrm{e}^{-1}$) of its initial value.

How can the RC time constant be found from a graph of charging capacitor voltage or charge?

Find the elapsed time for the quantity to rise to about 63% of its final value.

How can the initial tangent of an RC decay curve be used to find the time constant?

The tangent meets the zero level one time constant after the start.

How can the initial tangent of a rising RC charging curve be used to find the time constant?

The tangent meets the final-value level one time constant after the start.

What is the half-time of an exponentially decaying quantity in an RC circuit?

$T_{\frac12}=RC\ln 2\approx 0.69RC$. It is constant for a given circuit.

What happens to the remaining difference between a charging quantity and its final value over one half-time?

The difference is halved.