CAIE A-Level Physics A2: Capacitor Discharge

[Maximum number: 8]

Fig. 6.1 shows a capacitor of capacitance C connected in series with a resistor of resistance R.

Fig. 6.1

Initially the switch is open and there is a p.d. of 12 V across the capacitor.
At time t=0, the switch is closed so that there is a current I in the resistor.
Fig. 6.2 shows the variation of I with t.

Fig. 6.2

(a)

Explain the shape of the line in Fig. 6.2.

[ 3 ]

(b)

Use Fig. 6.2 to determine:

[ 3 ]

(i)

the time constant $\tau$ of the circuit in Fig. 6.1.

\begin{aligned} & \tau= \\ & \text { s [3] } \end{aligned}

[ 3 ]

correct read-off of at least one pair of values for I and t
attempted read-off of t when $I=0.048 \mathrm{~mA}$

or

substitution of a correct pair of values of I and t into $I=0.13 \exp (-t / \tau)$ $\tau=4.3 \mathrm{~s}$

(c)

Use your answers in (b) to determine capacitance C.

C =F [2]

[ 2 ]

$\tau=R C$ $\begin{aligned} C =\tau / R=4.3 /\left(9.2 \times 10^{4}\right) =4.7 \times 10^{-5} \mathrm{~F} \end{aligned}$

[Maximum number: 4]

A capacitor of capacitance $470 \mu \mathrm{~F}$ is connected to a battery of electromotive force (e.m.f.) 24 V in the circuit of Fig. 5.1.

Fig. 5.1

The two-way switch S is initially at position X.
P and Q are identical long straight wires, each with a resistance of $5.6 \mathrm{k} \Omega$ . These wires are placed near to, and parallel to, each other. Wire Q is connected to a voltmeter.

At time t=0, switch S is moved to position Y so that the capacitor discharges through wire P .

(a)

Calculate the current $I_{0}$ in wire P at time t=0.

I_{0}=

[ 1 ]

$\begin{aligned} I_{0} =24 / 5600 =4.3 \times 10^{-3} \mathrm{~A} \end{aligned}$

(b)

Calculate the time constant $\tau$ of the discharge circuit.

\tau=

[ 1 ]

$\tau=R C$ $\begin{aligned} =5600 \times 470 \times 10^{-6} =2.6 \mathrm{~s} \end{aligned}$

(c)

On Fig. 5.2, sketch a line to show the variation with t of the current I in wire P as the capacitor discharges.

Fig. 5.2

[ 2 ]

line with negative gradient throughout passing through ( $0, I_{0}$ )
exponential decay curve asymptotic to t-axis

[Maximum number: 8]

A capacitor, a battery of electromotive force (e.m.f.) 12 V , a resistor R and a two-way switch are connected in the circuit shown in Fig. 5.1.

Fig. 5.1

The switch is initially in position S . When the capacitor is fully charged, the switch is moved to position T so that the capacitor discharges. At time t after the switch is moved the charge on the capacitor is Q.

The variation with t of $\ln (Q / \mu C)$ is shown in Fig. 5.2.

Fig. 5.2

(a)

Show that the capacitance of the capacitor is $1.5 \mu \mathrm{~F}$ .

[ 3 ]

from graph $\ln Q=2.9$ $\text { (so } Q=18.2 \mu \mathrm{C} \text { ) }$
C=Q / V
$=18.2 / 12=1.5 \mu \mathrm{~F}$

(b)

Determine the resistance of R.

resistance =

[ 3 ]

gradient =-0.25
gradient =-1 / R C
$\begin{aligned} R =1 /\left(0.25 \times 1.5 \times 10^{-6}\right) =2.7 \times 10^{6} \Omega \end{aligned}$
or $\frac{Q}{Q_{0}}=e^{-t / C R}$ or $\ln Q-\ln Q_{0}=\frac{-t}{C R}$
e.g. $\frac{4.95}{18.2}=e^{-5.2 /\left(1.5 \times 10^{-6} R\right)}$ or $1.6-2.9=5.2 /\left(1.5 \times 10^{-6} R\right)$ $R=2.7 \times 10^{6} \Omega$

(c)

A second identical resistor is now connected in parallel with R.

The switch is initially in position S . When the capacitor is fully charged, the switch is moved to position T so that the capacitor discharges. At time t after the switch is moved the charge on the capacitor is Q.

On Fig. 5.2, sketch a line to show the variation of $\ln (Q / \mu \mathrm{C})$ with t between time t=0 and time $t=5.0 \mathrm{~s}$ .

[ 2 ]

straight line with different negative gradient starting from ( 0,2.9 )
straight line between t=0 and at least $t=5.0 \mathrm{~s}$ with twice the gradient of the original line

[Maximum number: 3]

Fig. 6.1 shows a capacitor of capacitance C connected in series with a resistor of resistance R.

Fig. 6.1

Initially the switch is open and there is a p.d. of 12 V across the capacitor.
At time t=0, the switch is closed so that there is a current I in the resistor.
Fig. 6.2 shows the variation of I with t.

Fig. 6.2

Explain the shape of the line in Fig. 6.2.

[Maximum number: 1]

A capacitor of capacitance $470 \mu \mathrm{~F}$ is connected to a battery of electromotive force (e.m.f.) 24 V in the circuit of Fig. 5.1.

Fig. 5.1

The two-way switch S is initially at position X.
P and Q are identical long straight wires, each with a resistance of $5.6 \mathrm{k} \Omega$ . These wires are placed near to, and parallel to, each other. Wire Q is connected to a voltmeter.

At time t=0, switch S is moved to position Y so that the capacitor discharges through wire P .

Calculate the time constant $\tau$ of the discharge circuit.

\tau=

$\tau=R C$ $\begin{aligned} =5600 \times 470 \times 10^{-6} =2.6 \mathrm{~s} \end{aligned}$

[Maximum number: 2]

A capacitor, a battery of electromotive force (e.m.f.) 12 V , a resistor R and a two-way switch are connected in the circuit shown in Fig. 5.1.

Fig. 5.1

The switch is initially in position S . When the capacitor is fully charged, the switch is moved to position T so that the capacitor discharges. At time t after the switch is moved the charge on the capacitor is Q.

The variation with t of $\ln (Q / \mu C)$ is shown in Fig. 5.2.

Fig. 5.2

A second identical resistor is now connected in parallel with R.

The switch is initially in position S . When the capacitor is fully charged, the switch is moved to position T so that the capacitor discharges. At time t after the switch is moved the charge on the capacitor is Q.

On Fig. 5.2, sketch a line to show the variation of $\ln (Q / \mu \mathrm{C})$ with t between time t=0 and time $t=5.0 \mathrm{~s}$ .

straight line with different negative gradient starting from ( 0,2.9 )
straight line between t=0 and at least $t=5.0 \mathrm{~s}$ with twice the gradient of the original line

CAIE A-Level Physics A2 19.3 Discharging a Capacitor Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (c)

Question 2

Question (a)

Question (b)

Question (c)

Question 3

Question (a)

Question (b)

Question (c)

Question 4

Question 5

Question 6