Troubles with a circuit analysis situation (RLC circuit)

[Anti Hydrogen]

Homework Statement

the book doesn't explain how they calculated the initial value of the voltage of the 2 ohms resistance and the inductor current; i understand, however, how they calculated the initial value of the capacitor. i think they are taking the voltage of the open circuit in left as zero so that the voltage of resistance takes the value of zero too; if so, why is the open circuit voltage zero?, the definition of open circuit according to the book says that voltage of a open circuit can be any value. note that the open circuit in the left of the circuit comes from a singularity funtion

Relevant Equations

please any help will be appreciated!

thanks

 

[gneill]

Hi Anti Hydrogen,

It's not entirely clear to me what you're asking. Is it for the voltage across the 2 Ω resistor at time t = 0⁺ ?

 

[Anti Hydrogen]

Hi Anti Hydrogen,

It's not entirely clear to me what you're asking. Is it for the voltage across the 2 Ω resistor at time t = 0⁺ ?

it is at t=0 minus

 

[Anti Hydrogen]

Hi Anti Hydrogen,

It's not entirely clear to me what you're asking. Is it for the voltage across the 2 Ω resistor at time t = 0⁺ ?

it is the initial value, this is, at t less than 0

 

[gneill]

Okay. Well, at t= 0^- there's no current being supplied by the current source, and no current due to the voltage source either (at steady state the capacitor looks like an open circuit). So, no current flowing anywhere. What does that tell you about the current through that resistor?

 

[Anti Hydrogen]

it's zero too, hence, the voltage across it is zero?

 

[gneill]

it's zero too, hence, the voltage across it is zero?

Yup.

 

[Anti Hydrogen]

.

Yup.

i calculated the voltage across the right open circuit applying the KVL in right mesh,
-20-vc=0
then
vc=-20
im i right?

 

[gneill]

Yes. At steady state the capacitor must have a potential difference that satisfies the KVL around the loop, but more obviously, since there's no current change through the inductor the potential at the top of the inductor with respect to the bottom of the inductor must be zero. Hence the sum of the voltage source and capacitor voltage must be zero.