PHYS-1500 PHYSICAL MODELING
FALL 2006
Circuit Elements II
If an inductor, a resistor, a capacitor and a source of emf (voltage) are put in a circuit, in series,
di
q
 iR   0 , or
dt
C
di
q
d 2 q dq
q
dq
E  L  iR  . However, we know that i 
, so this becomes, E  L 2 
R .
dt
C
dt
C
dt
dt
and the voltages are added up around the circuit, we get: E  L
The equation that we handled earlier for a mechanical system had the equation.
d 2x
dx
d 2x
dx
m 2   kx  b
 Fd , which can be written, Fd  m 2  b  kx . This has the same
dt
dt
dt
dt
form as the electrical equation, if the following identifications are made:
xq
mL
bR
k  1/C
FE
If the mechanical equation is divided by m, and the electrical equation is divided by L, they
F
d 2 x b dx k
E d 2 q R dq
q
 x , and  2 

become, d  2 
. The natural frequency of the
m dt
m dt m
L dt
L dt LC
k
mechanical system is given by  
. We can see that in the electrical system, the equivalent
m
quantity is given by  
1
.
LC
Therefore, with little modification, the program that worked for the mechanical system can be
used for the electrical system.