**UNIT
12**

**DIRECT
CURRENT CIRCUITS: CAPACITORS**

**Objectives**

· to understand how capacitors behave as elements in circuits

· to understand the definition of capacitance

· to understand how capacitors behave in series and parallel networks and be able to calculate the capacitance of series and parallel networks

** **

Equipment:

1 voltmeter

2 wires with alligator clips

1 battery

1 battery holder

1 capacitor

**1.1 **Consider a
capacitor connected to a battery as in the diagram below.

**a. **Discuss in terms
of charges and electric fields what happens. If current flows, describe why. Is
the current constant with time? Is it zero? Does it change? Is it the same in
different parts of the wire?

**b. **If after a long
time the capacitor were disconnected from the battery, would there be a net
charge on the capacitor?

**c. **Would there be a
reading on the voltmeter, if you attached a voltmeter across the capacitor?
Explain.

**d.** If, after the
capacitor has been disconnected from the battery, you connected one end of the
capacitor to a large piece of metal, what if anything would happen? Explain.

**e.** If, after the
capacitor has been disconnected from the battery, and you connected one end of
the capacitor to a large piece of metal, as in part **d**, would there be a
reading on a voltmeter, if you attached a voltmeter across the capacitor?
Explain.

**f. **Connect the
battery to the capacitor as in the diagram above. After the capacitor has been connected for
two minutes, disconnect the battery from the capacitor. Carry out the experiments described in parts **c**,**
d**,** **and **e** above. Explain.

Equipment:

None

**2.1 **

**a. **Is the potential
difference across the plates of a capacitor related to the amount of charge on
the plates? Explain.

**b. **The constant of
proportionality between the amount of charge on one of the plates and the
potential difference between the plates is called the capacitance:

_{}

The symbol for capacitance is C. The unit of capacitance is Farad (F). One Farad is equal to one Coulomb per Volt, 1F = 1C/V.

Equipment:

3 ammeter

8 wires with alligator clips

1 bulb

1 socket

1 battery

1 battery holder

1 switch

2 capacitor

1 nichrome wire

**3.1 **Consider the
following circuit.

**a.** Qualitatively,
what would the ammeters read as a function of time after the switch was closed?
Describe whether they would increase, decrease or remain the same. Would
ammeter 1 read the same as ammeter 2 sometimes? All the time? Explain.

**b. **Set up the circuit
and test your prediction.** **Explain the readings on the ammeters in terms
of charges and electric fields.

**3.2 **Consider the
following circuit.

**a.** Qualitatively,
what would the ammeters read as a function of time after the switch was closed?
Describe whether they would increase, decrease or remain the same. Would
ammeters 1, 2 and 3 read the same all the time? Sometimes? Explain your reasoning.

**b. **Set up the circuit
and test your prediction.** **Explain the readings on the ammeters in terms
of charges and electric fields.

Equipment:

None

**4.1 **Consider two** **capacitors
of different capacitances connected in parallel across a battery as shown
below.

**a.** Is the potential
difference between the plates of each capacitor the same? Explain. Do the two
capacitors have the same amount of charge on each of their plates? Explain.

**b. **How are the two**
**capacitors like a single capacitor?** **Could you replace the two
capacitors with a single capacitor? If so, what would be the charge, Q, on that
capacitor in terms of the charges (Q_{1} and Q_{2}) on the
original capacitors? Write this in terms
of an equation.

Use the equation that
relates the charge Q on the new capacitor to the charges Q_{1} and Q_{2}
and the relationship between charge and potential difference for each capacitor
to find the capacitance of the replacement capacitor in terms of the
capacitances C_{1} and C_{2} of the original two capacitors.

Discuss your relationship with an instructor.

**4.2 **Consider two** **capacitors
of different capacitances connected in series across a battery as shown below.

**a.** Do the two
capacitors have the same amount of charge on each of their plates? Explain. Is
the potential difference between the plates of each capacitor the same?
Explain.

**b. **How are the two**
**capacitors like a single capacitor?** **Could you replace the two
capacitors with a single capacitor? If so, what would be the potential
difference, DV, across the replacement
capacitor in terms of the potential differences across each of the original
capacitors? Write this in terms of an
equation.

Use the equation that
relates the potential difference DV on
the new capacitor to the potential differences DV_{1}
and DV_{2} and the relationship
between charge and potential difference for each capacitor to find the
capacitance of the replacement capacitor in terms of the capacitances C_{1}
and C_{2} of the original two capacitors.

Discuss your relationship with an instructor.

Equipment:

None

**3.1** A defibrillator
is a large capacitor.

When a defibrillator is discharged across a body, the current through the heart is about 6 amps. Compare this to the currents on the chart in the handout on the effect of different amounts of current on the human body. Explain.

**SUMMARY**

You should understand how capacitors behave as elements in circuits. You should understand the definition of capacitance. You should understand how capacitors behave in series and parallel networks and be able to calculate the capacitance of series and parallel networks.