### The Idea

A *capacitor* is an electronic component that can store an electrical charge. Unlike a battery that stores electrical charge through chemical reactions, the capacitor holds electrons on conductive plates separated by an insulator. Capacitors are present in numerous electronic circuits. They are also gaining attention recently as a possible means of supplementing batteries in electric cars. This experiment explores how capacitors can be charged and discharged.

### What You Need

- 1000 μF (micro-Farad) capacitor
- 50 kΩ (kilo-Ohm) resistor (note other capacitor/resistor combinations that can work are listed in Table 103-1)
- DC voltmeter (or multimeter configured as a voltmeter)
- 10-volt DC power supply
- DC ammeter (with 0–1.0 mA range)
- 3 knife switches (SW1, SW2, and SW3)
- jumper wire
- stopwatch
- 2 LEDs

### Method

### Charging

- Set up the circuit shown in Figure 103-1. Pay attention to the positive and negative polarity markings, especially if your capacitor has a designated positive side (some do and some don't). Start with all switches open.
- Close SW2. Leave open SW3.
- Close SW1 and start the timer.
- Record the current in mA every five seconds (this is easier with partners). If you miss a reading, keep going and catch the next five-second interval. Keep going until the current becomes too small to read. If other capacitor/resistor combinations are used, a different time interval than five seconds may be more appropriate.

### Discharging

- When the charging part is complete, open all the switches.
- Close SW1 and leave SW2 open.
- Close SW3 and start the timer.
- As before, record the current in five-second intervals.

### Expected Results

With SW2 closed, the capacitor will charge. LED2 will light, but slowly fades as the voltage builds and the current flow decreases. For the 10 kΩ resistor and the 1000 μF capacitor given in the parts list, the charging will be about two-thirds complete in 50 seconds, as shown in Figure 103-2.

With SW3 closed, the capacitor will discharge as indicated in Figure 103-3. After 50 seconds the voltage will have dropped from 10 volts to around 3.7 volts. LED3 will light and will slowly fade as the capacitor discharges.

In general, the time to charge or discharge two-thirds of capacity is characterized by the time constant. For a capacitor *C* (in Farads) and a resistor *R* (in ohms), the time constant, τ (in seconds), is given by τ = RC. The *time constant* represents the time where the current during charging or the voltage during discharging has decreased by about two-thirds. The following combinations of resistor and capacitor (Table 103-1) give a reasonable time constant of 30 seconds, which gives measurable results in this experiment.

### Why It Works

The current for a charging capacitor is given by *I* = I_{o}e^{–t/RC}

The voltage for a charging capacitor is given by *V* = V_{o}(1 – e^{–t/RC})

The current for a discharging capacitor is given by *I* = I_{o}e^{–t/RC}

The voltage for a discharging capacitor is given by V = V_{o}e^{–t/RC}

When t = the time constant, RC, then e^{–t/RC} = e^{–1} = 0.37. This mean a discharging capacitor has dropped to about one-third of its original value or has discharged about two-thirds.

### Other Things to Try

If you have other resistors and capacitors available, try (small) increases or decreases in values, and then determine how it affects the time to charge and discharge. The previous Table 103- 1 gives combinations that result in reasonable time constants and serves as a good starting point. Adjust your measurement interval as needed.

Use a current and voltage sensor that displays these parameters as a function of time on a computer. A combination voltage/current sensor (part number PS-2115) is available from PASCO that displays both parameters simultaneously in DataStudio software.

Make a graph of voltage (or current) versus time for your discharge data with voltage on a linear scale and time on a logarithmic scale. Use an exponential curve fit to an Excel scatter plot to find the argument of the exponent. Compare that with –1/RC.

### The Point

A capacitor is a device that stores electrical energy. The rate of charging and discharging depends on the size of the capacitor and the resistor it is charging or discharging through. The bigger the capacitor and the resistor, the longer these processes take. The charging and discharging is an exponential function of time that approaches a saturation value.

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