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 Experiments 2 and 3,
which of the following capacitance/resistance
combinations would result in the capacitor
storing 6 V of electrical energy in the greatest
amount of time?
A.
0.2 µF/10.0 MΩ
B.
1.2 µF/10.0 MΩ
C.
1.2 µF/2.5 MΩ
D.
0.2 µF/2.5 MΩ
The time it takes for the capacitor to store 6 V of electrical energy is inversely proportional to the product of capacitance and resistance, according to the formula t = RC (where t is the time, R is the resistance, and C is the capacitance).
By multiplying the values of capacitance and resistance for each combination, we get the following results:
A. 0.2 µF * 10.0 MΩ = 2 sec
B. 1.2 µF * 10.0 MΩ = 12 sec
C. 1.2 µF * 2.5 MΩ = 3 sec
D. 0.2 µF * 2.5 MΩ = 0.5 sec
Therefore, the combination that would result in the capacitor storing 6 V of electrical energy in the greatest amount of time is option B: 1.2 µF/10.0 MΩ.