Question: I am really unsure about how to go about this question and which circuits to consider.

Here's the question: 

Determine the value of the current labeled \$i\$ and the voltage labeled \$v\$ at \$t=0+\$, \$t=1.5ms\$, and \$t = 3.0ms\$.

The circuit is as follows: 

![schematic](https://i.stack.imgur.com/XrbPa.png)

[simulate this circuit](/plugins/schematics?image=http%3a%2f%2fi.stack.imgur.com%2fXrbPa.png) – Schematic created using [CircuitLab](https://www.circuitlab.com/)

Relevant equations:

Ohm's law: \$v = iR\$

Decay in source free RC Circuit \$v(t) = v(0) e^{-t/RC}\$

The attempt at a solution:

\$i(0-) = 0.1 A.\$

Therefore, 

\$v\$ across 200 ohm: \$200 \* 0.1 = 20 V\$

Since no current flows through capacitor with constant dc current,

\$v\$ across capacitor: \$20 V @ t < 0\$

\$v\$ across capacitor cannot change immediately as it would require infinite power so \$v\$ across capacitor @ \$t = 0\$ is \$20V\$

Here's where the confusion is: Should I include the 200 ohm resistor in my RC circuit? Why or why not? Also, will my circuit be a source free RC circuit?

Also, what will be the current i through the 200 ohm resistor when t>0?

My last question is a theoretical one: Can a current through a resistor change immediately at one instant of time?

Answer: 
When solving problems like this, it is helpful to draw the two *different* circuits that exist before and after \$t=0\$.

Before, with the switch open, since the circuit is in DC steady state, replace the capacitor with an open circuit and then it is easy to solve for \$v\_C(0)\$, the initial condition.

After, with the switch closed, the current source and 200 \$\Omega \$ resistor are paralleled with a short circuit and so, from the perspective of the capacitor, can be *ignored* (a short circuit in parallel with any other circuit elements is equivalent to a short circuit).

So, the circuit after \$t=0\$ is just the capacitor and the 50 \$\Omega \$ resistor, a simple RC circuit with initial condition \$v\_C(0)\$.

> 
> Also, what will be the current i through the 200 ohm resistor when
>  t>0?
> 
> 
> 

With a short circuit in parallel, the voltage across the resistor is ?V and, using Ohm's law, the current is ?A.

> 
> My last question is a theoretical one: Can a current through a
>  resistor change immediately at one instant of time?
> 
> 
> 

Theoretically, within ideal circuit theory, the answer is yes. In reality, the answer is no. for example, physical resistors have associated "parasitic" capacitance and inductance.
at t=0 the equivalent circuit is very simple.

![enter image description here](https://i.stack.imgur.com/JpfmD.jpg)

Since the switch is ideal, it will have 0V drop circulating all the current source and thus closing the path out of the circuit.

Thus the 20V initial condition discharges with an RC time constant of 20uF\*50R=1000 uS.

Did anyone actually guess the answer at 1.5mS and 3mS is 5V(~25%) and 1V(~5%) respectively for the exponential decay from 20V to 0V?