Passage III

An electrical circuit contained a 12-volt (V) battery, a resistor (a device that resists the flow of electricity), a capacitor (a device that stores electrical charge and electrical energy), a voltmeter (an instrument for measuring voltage), and a switch, as shown in Figure 1.

Some students studied the behavior of the circuit.

Experiment 1

The students used a 1 × 107 ohm (Ω) resistor and a capacitor with a capacitance of 1 × 10–6 farad (F). (Capacitance is a measure of the maximum amount of electrical charge and electrical energy a capacitor can store.) The capacitor was initially uncharged. At time zero, the students simultaneously closed the switch and started a stopwatch. At time zero and at 12 sec intervals thereafter, they recorded the voltage across the capacitor. Their results are shown in Table 1.

Experiment 2

Using the 1 × 107 Ω resistor and several different capacitors, the students determined the length of time from when the switch was closed until the voltage across the capacitor reached 6 V. Their results are shown in Table 2.

Experiment 3

The students conducted the same procedure described in Experiment 2, except that they used a constant capacitance of 1 × 10–6 F and several different resistors. Their results are shown in Table 3.

15. If, in Experiment 2, a 1.5 × 10–6 F capacitor had been used, the time required for the voltage across the capacitor to reach 6 V would have been closest to:

Answer and Explanation

Your Answer is

Correct Answer is C

Explanation

Looking at table 2, as the capacitance becomes smaller, the time to reach 6 V also becomes smaller, and the time to reach 6 V will increase by 2.1 sec for every increase in capacitance of 0.3×10-6. The capacitance given in the question stem is 1.5×10-6, which is larger than 1.2×10-6, so the time needs to be longer than 8.3 sec, which should be about 8.3+2.1=10.4 sec, 10.5 sec of option C is closest