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i got stuck in finding the diif equation for this circuit

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i have one node circuit

a voltage source a ressistor and a capacitor are linked point by point
in a circle way.

so i did
kvl
[latex]
E-V_R-V_c=0
[/latex]
[latex]
I_c=I_R
[/latex]
i am not getting a diff equation here
the only way to make a diff equation is some how use
[latex]
I=c\dot{v_c}
[/latex]

??
 

ericgibbs

Well-Known Member
Most Helpful Member
i have one node circuit

a voltage source a ressistor and a capacitor are linked point by point
in a circle way.

so i did
kvl
[latex]
E-V_R-V_c=0
[/latex]
[latex]
I_c=I_R
[/latex]
i am not getting a diff equation here
the only way to make a diff equation is some how use
[latex]
I=c\dot{v_c}
[/latex]

??
hi,
The voltage increase on the capacitor is an exponential increase.
 

MrAl

Well-Known Member
Most Helpful Member
Hi again,


It appears that you are having a problem formulating the differential
equations for some circuits.

For this circuit, we have a resistor in series with a capacitor in series with
a positive voltage source (relative to ground on one end of the cap).

First, recall the time equation for the capacitor:

C*dv/dt=i

which simply relates current 'i' to the first derivative.
Now since the cap is in series with the resistor, and the
resistor voltage is R*i, and we know the current in the cap
is i=C*dv/dt (above) we can write the voltage across the
resistor as R*C*dv/dt, and that means of course the voltage
across the cap is simply v, and since the source voltage is
a constant E, we can write:

E=R*C*dv/dt+v

so we end up with an equation in v(t) and its derivative,
and once we solve that differential equation (using whatever method)
we get the time solution to the problem of what the capacitor voltage is.

I think you may wish to review the relationships between current and voltage
for the resistor, capacitor, and inductor:

v=R*i
C*dv/dt=i
v=L*di/dt

These are the most important relationships.

What is sometimes not obvious when writing the equations for circuits is if we know one
variable (either i or v) for an element, that usually means we automatically know the
other variable (v or i). This isnt always obvious but we should be on the lookout for
this kind of thing that results in many simplifications.
For example, in the series RC circuit we just looked at we could say that we knew what
'i' was if we pretended to know what dv/dt for the cap was when we wrote the equation.
Of course we dont really know until we solve it, but we write the equation as if we already
knew what it was, then later we actually do find it.
 
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