IB Physics SL B.5 Current and circuits questions

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Question 1

Multiple choiceMedium1 mark

A resistor is tested by increasing the potential difference across it and recording the current. The measured values are plotted.

Which row identifies the resistor’s behaviour and gives the ratio of power dissipated at B to that at A?

Show answer and explanation

Answer: C. At A, $V/I=2.0/0.40=5.0\ \Omega$ at B, $V/I=5.0/0.80=6.25\ \Omega$ Since the resistance is not constant, the behaviour is non-ohmic. Using $P=IV$ $P_A=0.80\ \mathrm{W}$ and $P_B=4.0\ \mathrm{W}$ so $P_B/P_A=5.0$

A: obtains the power ratio but treats the unequal $V/I$ values as equal, classifying the resistor as ohmic.
B: uses the current ratio, $0.80/0.40=2.0$ as the power ratio and omits the change in potential difference.
D: assumes constant resistance and uses $P\propto I^2$ giving a ratio of $4.0$

Remember: compare $V/I$ to identify ohmic behaviour, and use $P=IV$ for power at each operating point.

Question 2

Multiple choiceMedium1 mark

Two resistors of resistance $R$ and $2R$ are connected in series across an ideal source of potential difference $V$ They are then connected in parallel across an identical ideal source. What is the ratio of the current through the $R$ resistor in the series arrangement to the current through the $2R$ resistor in the parallel arrangement?

Show answer and explanation

Answer: B. In series, the total resistance is $3R$ so the current through $R$ is $V/(3R)$ In parallel, the $2R$ resistor has the full potential difference $V$ so its current is $V/(2R)$ The required ratio is $[V/(3R)]/[V/(2R)]=2/3$ A: uses the current through the $R$ branch in parallel, $V/R$ as the denominator. C: assumes the currents are equal because the source potential differences are equal. D: omits the $2R$ resistor when finding the series resistance, giving a series current of $V/R$ Remember: series current depends on the total resistance, while each parallel branch has the full source potential difference.

Question 3

Paper 2Hard10 marks

Two samples, $X$ and $Y$ have the same length and cross-sectional area. Sample $X$ is a metal; sample $Y$ is an unknown material. Each sample is connected separately to a variable d.c. supply. The potential difference $V$ across the sample and the current $I$ through it are measured at the same temperature.

(a)

Using Figure 1, read the current in each sample when the potential difference is $3.0\ \text{V}$

[2]

(b)

Use the reading for sample $X$ at $3.0\ \text{V}$ to determine its resistance.

[2]

(c)

A third test uses a sample $S$ which is either $X$ or $Y$ It is connected in series with a $50\ \Omega$ resistor to a $6.0\ \text{V}$ supply. The current in the circuit is $60\ \text{mA}$ Use the circuit information and Figure 1 to determine whether $S$ matches $X$ or (Y). Show your reasoning.

[4]

(d)

A student claims that sample $Y$ has no mobile charge carriers because its current is almost zero. Assess this claim using Figure 1 and the idea of mobility of charge carriers.

[2]

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