The topic of this problem is Energy Storage Elements.

The problem is to find R, the resistance in our circuit,

if v1(t) = 1e to the -200t V for t greater than or equal to 0.

So if we look at our circuit below, it has two sources, a voltage source on the left

hand side and a current source on the right hand side of the circuit.

Our voltage v1 is the voltage that's dropped across the 50 ohm resistor at

the top of the circuit.

And the resistance that we're looking for

is the resistor that connects the top and the bottom of our circuit as shown.

So how do we find that resistance?

We can use a number of different methods to find it.

Perhaps the easiest way to do this is to use Kirchhoff's Voltage Laws and

sum the voltages around this loop.

So if we sum the voltages around this loop,

the sum has to be equal to 0 at any instant in time.

We alternative could have looked at another circuit, or another mesh, and

perhaps looked at the right side of the mesh and try to do something with it, but

what we would find is we don't know the voltage across this current source.

So if we try to use Kirchhoff's Voltage Law on this

right hand side of the circuit, we'd have to introduce an additional variable for

the voltage drop across this current source.

And ultimately that would give us too many unknowns for

the number of equations that we can generate.

So if we look at this, again, left most loop and sum the voltage around it,

then that should give us at least one equation that we could look at to see if

we can resolve R from our knowledge.

So starting in the lower left hand corner of this loop, and

again, summing the voltages around this loop, we would have,