Learning Goal: To understand how to calculate capacitance, voltage, and charge f
ID: 1427483 • Letter: L
Question
Learning Goal:
To understand how to calculate capacitance, voltage, and charge for a parallel combination of capacitors.
Frequently, several capacitors are connected together to form a collection of capacitors. We may be interested in determining the overall capacitance of such a collection. The simplest configuration to analyze involves capacitors connected in series or in parallel. More complicated setups can often (though not always!) be treated by combining the rules for these two cases. Consider the example of a parallel combination of capacitors: Three capacitors are connected to each other and to a battery as shown in the figure.(Figure 1)The individual capacitances are C, 2C, and 3C, and the battery's voltage is V.
a-) If the potential of plate 1 is V, then, in equilibrium, what are the potentials of plates 3 and 6? Assume that the negative terminal of the battery is at zero potential.
If the potential of plate 1 is , then, in equilibrium, what are the potentials of plates 3 and 6? Assume that the negative terminal of the battery is at zero potential.Choose below.
V2 and V3
b-) If the charge of the first capacitor (the one with capacitance C) is Q, then what are the charges of the second and third capacitors?
If the charge of the first capacitor (the one with capacitance ) is , then what are the charges of the second and third capacitors? Choose below.
0 and 0
c-) Suppose we consider the system of the three capacitors as a single "equivalent" capacitor. Given the charges of the three individual capacitors calculated in the previous part, find the total charge Qtot for this equivalent capacitor.
Express your answer in terms of V and C.
D-) Using the value of Qtot, find the equivalent capacitance Ceq for this combination of capacitors.
Express your answer in terms of C.
V and V 2V and 3V V and 0V2 and V3
b-) If the charge of the first capacitor (the one with capacitance C) is Q, then what are the charges of the second and third capacitors?
If the charge of the first capacitor (the one with capacitance ) is , then what are the charges of the second and third capacitors? Choose below.
2Q and 3Q Q2 and Q3 Q and Q0 and 0
c-) Suppose we consider the system of the three capacitors as a single "equivalent" capacitor. Given the charges of the three individual capacitors calculated in the previous part, find the total charge Qtot for this equivalent capacitor.
Express your answer in terms of V and C.
D-) Using the value of Qtot, find the equivalent capacitance Ceq for this combination of capacitors.
Express your answer in terms of C.
Explanation / Answer
a) potential on plate3 is V
potential on plate 6 is 0
b)Q=C*V
charge on first is Q= CV
charge on second =2CV = 2Q
charge on third capacitance = 3CV =3Q
hence option 1 is correct
c) total charge Qtotal= Q1+Q2+Q3 = Q+2Q+3Q = 6Q
d) Qtotal = Cequuivalent *V
Cequuivalent =Qtotal / V = 6Q/V = 6C ............ since(C=Q/V)
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