Discussion Question 5A
P212, Week 5
Analysis of Capacitor Networks
In this discussion question, we will study a classic problem of the type that you will encounter
frequently in circuit analysis. But before we attack
...
Discussion Question 5A
P212, Week 5
Analysis of Capacitor Networks
In this discussion question, we will study a classic problem of the type that you will encounter
frequently in circuit analysis. But before we attack the full problem, we need to understand the basic
concepts of how to analyze capacitors in series and in parallel.
(a) The diagram at right shows a battery of voltage V0 hooked up to
two capacitors with capacitance C1 and C2 connected in parallel.
Find the expression of capacitance that combines the two
capacitors into one equivalent capacitor C12.
(Hint: If capacitor C1 has charge Q1 and capacitor C2 has charge Q2, how much charge is contained
in the equivalent capacitor C12? What is DV12 across this equivalent capacitor?)
(b) Generalizing part (a) to n parallel capacitors, find the expression of capacitance that combines the
n capacitors into one equivalent capacitor between point A and B.
(c) The diagram at right shows a battery of voltage V0 hooked up to two capacitors with capacitance
C1 and C2 connected in series. Find the expression of capacitance that combines the two
capacitors into one equivalent capacitor C12.
(Hint: Suppose capacitor C1 has charge Q1 and capacitor C2 has
charge Q2. What is the restriction on Q1 and Q2 ?
How much charge is contained in the equivalent capacitor C12?
What is DV12 across this equivalent capacitor?)
(d) Find the expression of capacitance that combines n capacitors in series, with capacitance C1, C2 , …,
Cn, into one equivalent capacitor.
V0
C1 C2
V0 C1
C2
The top plates of a and Cz are connected and thus have
the same potential as do the bottom plates Thus 04 04 4
Q lot CiaVo QitQa C Vo 1 Cabo C
Mathematical induction
Ce
In this case the two capacitors have the same change
say Q and to out ok 1
L the az T
The n capacitors have the same charge and
Vo out OVzt to Vu In I t f t tf
Hence https://www.coursehero.com/file/74870474/problemsetsolutions5pdf/ Ian ft'Et 5
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