UCSD Summer Session
Physics 2B Formula Sheet
UNIT 2 –Capacitor & Network (combo) Supplement
Three macroscopic parameters completely define how a capacitor behaves in a circuit:
the Capacitance C, the applied Potential V, and Charge Q. They are always related by
Q = CV
Capacitor Equation
We connect Capacitors together into networks in different ways. The basic building blocks
are SERIES and PARALLEL. These in turn can be joined to make more complicated
circuits.
In these configurations, one equivalent capacitor CEquiv can replace them all, and we can use
the same equation for the equivalent. When we do so, we may still be interested the C, V, and
Q of each of the individual elements. The following table summarizes the characteristics for
the two types of networks.
Of course, one can combine these into more complicated networks, but the same rules apply.
Supplementary Capacitor Circuit Table
Parallel
Schematic Diagram
Series
C1
C1
C2
C2
C3
C3
1
1
1
1
+
+
+"
CSeries C1 C2 C3
1
CSeries = × C
n
=
Equivalent Capacitance
CParallel = C1 + C2 + C3 +"
Equivalent Shortcut for
Identical Capacitors
CParallel = n × C
Potential (Voltage)
V1 = V2 = V3 " = Vcircuit
V1 + V2 + V3 + " = Vcircuit
Charge
Q1 + Q2 + Q3 + " = Qcircuit
Q1 = Q2 = Q3 " = Qcircuit
Ratios
Q
Q1 Q2 Q3
=
= " = circuit
C1 C2 C3
C parall
C1V1 = C2V2 = C3V3 " = CcirVcir
The Potential line follows from the properties of equipotentials.
In parallel, the ratio of charges is the direct ratio of the capacitances.
In series, the ratio of the voltages is the inverse ratio of the capacitances.
IMPORTANT!!!
The Capacitor Equation applies only to the values of one device at a time.
This is why we “reduce” more complicated circuits to one equivalent device.