Students in science class designed the

Question

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.

Answer 1

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.