Circuits 2021 Series/Parallel/Resistance

A voltmeter must be connected in parallel with a circuit component to correctly measure the potential difference across the component. Which of the following explains why the voltmeter should have a very large resistance?

• A large resistance is needed to make sure the voltmeter has the same current through it as the circuit component, so the potential difference across the voltmeter is the same as that across the component.

• A large resistance is needed to make sure a large current passes through the voltmeter, so the rest of the circuit is not affected.

• A large resistance is needed to make sure negligible current passes through the voltmeter, so the rest of the circuit is not affected

• A large resistance is needed to make sure the current through the voltmeter has the same nonnegligible value whenever it is used, regardless of the current in the rest of the circuit.

A student has several conducting rods made from the same material. The rods have the same length but different square cross-sectional areas. The student places the rods in a circuit so that they have the same potential difference across them and then measures the current in each conducting rod. Which of the following graphs most likely contains a best-fit line to the graph of the current I as a function of the crosssectional area A of the rods?

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A wire of known dimensions is connected to a power source set to a low potential difference. The current through the wire is measured, and its resistance is calculated. The power source is set to a very high potential difference, and the measurement and calculation are repeated. Must the two calculated resistance values always be the same, and why or why not?

• No, because a change in potential difference does not affect the properties of the wire.

• No, because if the wire heats up enough, its resistivity may change significantly.

• Yes, because the wire dimensions have not changed.

• Yes, because according to Ohm’s law, the resistance is a constant of proportionality between V and I

A student collected the data shown above for the potential difference across a resistor and the corresponding power it dissipates. Which of the following best represents the data?

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A student wants to investigate how different values of resistance affect the total current in a circuit when the resistors are connected in parallel. Which of the following circuits will allow the student to do this?

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Students measure the potential across a lightbulb and the current through it using the circuit shown above. The results are shown in the graph. Which of the following is supported by evidence from the graph?

• The brightness of the lightbulb is proportional to the square of the current

• The brightness of the lightbulb is not proportional to the square of the potential difference

• The resistance of the lightbulb for each data point can be determined by dividing the potential difference by the current.

• The resistance of the lightbulb is not constant.

Four resistors are connected to a power supply, as shown above. The potential difference across the 10 ohm resistor is 4V. A student says that the potential difference across resistor R is 32V. Is the student correct, and why or why not?

• Yes. There is a loop that contains just R and the 10 ohm resistor. The potential difference across R plus that across the 10 ohm resistor will equal the power supply emf. Therefore, the potential difference across resistor R is 36V - 4V = 32V.

• No. The 10 ohm and 6 ohm resistors are in parallel, so they have the same potential difference. There is a loop that contains R and both the 10 ohm and 6 ohm resistors. So the potential difference across the 10 ohm resistor plus that across the 6 ohm resistor plus that across resistor R will equal the power supply emf. Therefore, the potential difference across resistor R is 36V - 4V - 4V = 28V.

• No. The 10ohm, 6 ohm, and 4 ohm resistors are in parallel, so they have the same potential difference. They are in series with resistor R, so the potential difference across each of the three parallel resistors plus that of resistor R will equal the power supply emf. Therefore, the potential difference across resistor R is 36V - 4V - 4V - 4V = 24V.

• No. All four resistors are in parallel, so they will all have the same potential difference. So the potential difference across is equal to 4V.

The figure above shows a battery of emf E and negligible internal resistance connected in series with resistors 1, 2, and 3, which have resistances R1, R2, and , R3 respectively. The resistance R1 can be varied. Which of the following diagrams correctly shows how a voltmeter V and an ammeter A could be connected to measure the potential difference across and the current in resistor 3 ?

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In the circuit shown above, what is the current in resistor R?

• 3A

• 6A

• 7A

• 9A

The circuit above contains five identical lightbulbs and a battery. Which of the following are correct about the current in the circuit? Select two answers.

• As the current travels clockwise around the circuit through lightbulb 1, then 2, then 5, it decreases

• The sum of the currents in lightbulbs 1, 3, 4, and 5 equals the current through the battery

• The current in lightbulb 1 is greater than the current in lightbulbs 2, 3, and 4

• The currents in lightbulbs 1 and 5 are the same