AP® Physics C: E&M - Simple Circuits - FRQs
Question
The circuit shown above consists of a source of variable emf ε , an ideal ammeter A, an ideal voltmeter V, a resistor of resistance R, and a sample of wire with resistance r.
(a) How does the current through the wire sample compare with the current through the resistor R ?
__________It is greater through R. __________It is greater through the sample.
__________It is the same through both. __________It depends on the resistance of the sample.
Justify your answer.
(b) How does the potential difference across the wire sample compare with the potential difference across the resistor R ?
__________It is greater across R. __________It is greater across the sample.
__________It is the same across both. __________It depends on the resistance of the sample.
Justify your answer.
With the sample of wire in place, the emf of the source is set to a given value. The current through and potential difference across the resistor R are measured. This is repeated for several values of emf, and the data are recorded in the table below.
| ε ( V) | VR (V) | IR (A) | ||
| 0.250 | 0.179 | 0.162 | ||
| 0.500 | 0.335 | 0.327 | ||
| 0.750 | 0.520 | 0.490 | ||
| 1.000 | 0.670 | 0.687 |
(c) Indicate below which quantities should be graphed to yield a straight line that could be used to calculate a numerical value for the resistance of the wire sample.
Horizontal axis: __________
Vertical axis: __________
You may use the remaining columns in the table above, as needed, to record any quantities that you indicated that are not given.
(d) On the grid below, plot the straight line data points from part (c). Clearly scale and label all axes, including units if appropriate. Draw a straight line that best represents the data.
(e) Use your straight line to calculate the value of the resistance of the wire sample.
(f) The wire sample has a length of 3.00 m and a radius of 1.00 × 10-3 m . Calculate the resistivity of the material from which the wire sample is made.
(g)
i. Suppose the ammeter used to collect these data was not ideal. Would the actual value of the resistance of the wire sample be greater than, less than, or equal to that calculated in part (e) ?
________Greater than ________Less than ________Equal to
Justify your answer.
ii. If the ideal voltmeter is replaced by a voltmeter that is not ideal and the experiment is repeated, would the readings of the ideal ammeter be greater than, less than, or equal to those in the data chart before part (c) ?
________Greater than ________Less than ________Equal to
Justify your answer.
Answer/Explanation
Ans:
(a)
_____√_____It is the same through both.
In a series circuit, the amount of current going through each component in the series is the same.
(b)
_____√_____It depends on the resistance of the sample.
Based on the Law that V = IR, since I is the same through R and r in the series circuit, the potential difference across each segment depends on R and r.
| ε ( V) | VR (V) | IR (A) | ε – VR (V) | |
| 0.250 | 0.179 | 0.162 | 0.071 | |
| 0.500 | 0.335 | 0.327 | 0.165 | |
| 0.750 | 0.520 | 0.490 | 0.230 | |
| 1.000 | 0.670 | 0.687 | 0.330 |
(c) Indicate below which quantities should be graphed to yield a straight line that could be used to calculate a numerical value for the resistance of the wire sample.
Horizontal axis: _____IR_____ ε – VR – IR . r =0
Vertical axis: _____ε – VR __ \(\frac{\varepsilon -V_{R}}{I_{R}}= r\)
(d)
(e)
slope = \(\frac{0.3-0.23}{0.64-0.49}=\frac{0.07}{0.15}=0.4667\Omega = \frac{\varepsilon -V_{R}}{I_{R}} = r\)
(f)
\(r = \frac{\rho l}{A}\) \(\rho = \frac{r.A}{l}= \frac{(0.4667)\left ( \pi \cdot (1\times 10^{-3})^{2} \right )}{3}\)
\(\rho = 4.88 \times 10^{7}\Omega m\)
(g)
(g)
i. Suppose the ammeter used to collect these data was not ideal. Would the actual value of the resistance of the wire sample be greater than, less than, or equal to that calculated in part (e) ?
______Greater than ____√____Less than ________Equal to
If the ammeter was not ideal, it would have a resistance greater than zero, but we assumed all of the resistance from the wire came from the wire sample, so actually some of the resistance belongs to the ammeter, not completely to the wire sample.
ii. If the ideal voltmeter is replaced by a voltmeter that is not ideal and the experiment is repeated, would the readings of the ideal ammeter be greater than, less than, or equal to those in the data chart before part (c) ?
___√____Greater than ________Less than ________Equal to
A non-ideal voltmeter would decrease the resistance in the circuit (due to the parallel structure) so there would be more current drawn from the battery.