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Study B.5 Current and circuits conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 8]

This question is in two parts. Part 1 is about a thermistor circuit. Part 2 is about vibrations and waves.
Part 1 Thermistor circuit
The circuit shows a negative temperature coefficient (NTC) thermistor X and a $100 \mathrm{k} \Omega$ fixed resistor R connected across a battery.

The battery has an electromotive force (emf) of 12.0 V and negligible internal resistance.

(a)

Define electromotive force (emf).

[ 1 ]

(b)

The graph below shows the variation with temperature T of the resistance $R_{\mathrm{x}}$ of the thermistor.

[ 7 ]

(i)

Determine the temperature of X when the potential difference across R is 4.5 V .

[ 4 ]

$V_X=7.5\,\mathrm{V}$ $I=\frac{4.5\,\mathrm{V}}{100\times10^3\,\Omega}=4.5\times10^{-5}\,\mathrm{A}$ $R_X=\frac{7.5\,\mathrm{V}}{4.5\times10^{-5}\,\mathrm{A}}=1.67\times10^5\,\Omega$ $T=-37\text{ to }-38\,^{\circ}\mathrm{C}$

Alternatively, use the potential-divider relation V_X/V_R=R_X/R_R or the equivalent resistance calculation.

(ii)

State the range of temperatures for which the change in the resistance of the thermistor is most sensitive to changes in temperature.

[ 1 ]

50 to (up to) $-30^{\circ} \mathrm{C} /$ at low temperatures;

(iii)

State and explain the effect of a decrease in temperature on the ratio

\frac{\text { voltage across } \mathrm{X}}{\text { voltage across } \mathrm{R}}

Part 2 Vibrations and waves

The cone and dust cap D of a loudspeaker L vibrates with a frequency of 1.25 kHz with simple harmonic motion (SHM).

Figure for Question (iii) — IB Physics SL

[ 2 ]

as the temperature decreases $R_{X}$ increases;
same current through R and X so the ratio increases or $V_{X}$ increases and $V_{R}$ decreases so the ratio increases;

Part 2 Vibrations and waves

[Maximum number: 10]

(a)

A cell is connected to an ideal voltmeter, a switch S and a resistor R. The resistance of R is $4.0 \Omega$ .

When S is open the reading on the voltmeter is 12 V . When S is closed the voltmeter reads 8.0 V .

[ 3 ]

(i)

State the emf of the cell.

[ 1 ]

$12 \mathrm{~V}$

(ii)

Deduce the internal resistance of the cell.

[ 2 ]

I=2.0 A OR 12=I(r+4) OR 4=I r OR 8=4 I

«Correct working to get » r=2.0 « $\Omega$ »

Marking guidance:

Allow ECF from (b)(i)

(b)

The voltmeter is used in another circuit that contains two secondary cells.

Cell A has an emf of 10 V and an internal resistance of $1.0 \Omega$ . Cell B has an emf of 4.0 V and an internal resistance of $2.0 \Omega$ .

Calculate the reading on the voltmeter.

[ 3 ]

(c)

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions $0.40 \mathrm{~m} \times 0.15 \mathrm{~m}$ at a place where the maximum intensity of sunlight is $380 \mathrm{Wm}^{-2}$ .

The overall efficiency of the re-charging process is 18 %.
Calculate the minimum time required to re-charge the cell fully.

[ 3 ]

ALTERNATIVE 1

«energy output of the panel = » VIt OR $6 \times 5 \times 0.25 \times 3600$ OR 27000 «J»

«available power => $380 \times 0.4 \times 0.15 \times 0.18$ OR 4.1 «W»

$t=\ll \frac{27000}{4.1}=>6600<\mathrm{S} \gg$

ALTERNATIVE 2

«energy needed from Sun = » $\frac{V I t}{\text { eff }}$ OR $\frac{6 \times 5 \times 0.25 \times 3600}{0.18}$ OR 150000 «J»

« incident power=» $380 \times 0.4 \times 0.15$ OR 22.8 «W»

$t=\ll \frac{150000}{22.8}=>6600<\mathrm{S} \gg$

Marking guidance:

Allow ECF for MP3

Accept final answer in minutes (110) or hours (1.8).

(d)

Outline why research into solar cell technology is important to society.

[ 1 ]

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IB Physics SL B 5 Current and Circuits Topic Practice

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Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (c)

Question (d)