Consider the combination of capacitors shown in the figure.(Figure 1) Three capa
ID: 2286471 • Letter: C
Question
Consider the combination of capacitors shown in the figure.(Figure 1) Three capacitors are connected to each other in series, and then to the battery. The values of the capacitances are C, 2C, and 3C, and the applied voltage is ?V. Initially, all of the capacitors are completely discharged; after the battery is connected, the charge on plate 1 is Q.
1. What are the charges on plates 3 and 6?
2. If the voltage across the first capacitor (the one with capacitance ) is , then what are the voltages across the second and third capacitors?
3. Find the voltage ?V1 across the first capacitor. Express your answer in terms of ?V.
4. Find the charge Q on the first capacitor. Express your answer in terms of C and ?V1.
5. Using the value of Q just calculated, find the equivalent capacitance Ceq for this combination of capacitors in series. Express your answer in terms of C.
+Q and +Q ?Q and ?Q +Q and ?Q ?Q and +Q 0 and +Q 0 and ?QExplanation / Answer
1) the charges on plates 3 and 6 are +Q and -Q
Correct answer is C.+Q and -Q
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2) When capacitors are connected in series, the charge on each is same and equal to total charge stored
In series combination, the potential across any capacitor is inversly proportional to its capacity
If the voltage across the first capacitor (the one with capacitance C) is V', then
V'=Q /C
The voltage across second capacitor =Q/2C =(1/2)Q/C=V'/2
The voltage across third capacitor =Q/3C =(1/3)Q/C=V'/3
Correct answer is B.V'/2 and V'/3
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V= V_1 +V_2+V_3
V= V_1 +V_1/2+V_1/3
V = 11V_1/6
3 .The voltage V_1 across the first capacitor= V_1= 6V/ 11
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4 The charge Q on the first capacitorQ = cV_1
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V= V_1 +V_2+V_3
Q/C_eq =Q/c +Q/2c +Q/3c
1/C_eq =1/c +1/2c +1/3c
5 The equivalent capacitance C_eq for this combination of capacitors in series.
C_eq =6c /11