Students in science class designed the
electrical circuit shown in the figure below. The
circuit consists of a 12-volt (V) battery, a switch, a
capacitor (a two-plate electrical storage device), a
voltmeter (an instrument capable of measuring the
electrical potential difference between two points in
an electric circuit), and a resistor (a two-terminal
electronic device that resists the flow of electricity
in a circuit).
The students performed three experiments
using this electrical circuit.
Experiment 1
The students used a 10 megohm (MΩ)
resistor and a capacitor with a capacitance of 1
microfarad (µF). (Capacitance is the measure of the
maximum amount of electrical energy that a given
capacitor can store.) At the beginning of the ex-
periment (“time zero”) the capacitor was uncharged.
To begin the experiment, one student closed the
switch while another simultaneously started a timer.
At time zero, and at 10-second intervals thereafter, a
third student recorded the values from the
voltmeter. The results are set forth in Table 1.
Table 1
Time (sec) Voltmeter reading (V)
0
10
20
30
40 0.0
7.8
10.4
11.6
12.0
Experiment 2
The students used a 10 MΩ resistor and 5
different capacitors, each having a unique
capacitance. For each of the 5 capacitors, the
students used the voltmeter to determine the length
of time it took the uncharged capacitor to store 6
volts of electrical energy. The results are set forth
in Table 2.
Table 2
Capacitance (μF) Time for capacitor to
store 6 V of
electrical energy (sec)
1.2
1.0
0.6
0.4
0.2 7.2
6.0
3.6
2.4
1.2
Experiment 3
The students used a capacitor with a
capacitance of 1µF and 4 different resistors, each
having a unique resistance. For each of the 4
resistors, the students used the voltmeter to
determine the length of time it took the uncharged
capacitor to store 6 volts of electrical energy. The
results are set forth in Table 3.
Table 3
Resistance (MΩ) Time for capacitor to
store 6 V of
electrical energy (sec)
10.0
7.5
5.0
2.5 6.0
4.5
3.6
1.9
Based on the results of Experiment 1, approx-
imately how long, from time zero, did it take the
voltmeter to reach a reading of 10.7 V?
A.
Less than 10 sec.
B.
Between 10 and 20 sec.
C.
Between 20 and 40 sec.
D.
More than 40 sec.
To determine approximately how long it took the voltmeter to reach a reading of 10.7 V, we can infer from the table provided in Experiment 1. We can see that the voltmeter reading increased from 7.8 V at 10 seconds to 10.4 V at 20 seconds, suggesting a linear increase.
If we interpolate between the provided data points, we can estimate that the reading would be around 10.7 V at approximately 15-16 seconds. Therefore, the correct answer is:
B. Between 10 and 20 sec.