- 5

- 0

**1. Homework Statement**

Find the general solution for the current I(z,t) associated with the voltage V(z,t).Do this by substituting [1] in to [2] and [3], integrate with respect to time, and then take the derivative with respect to z.

**2. Homework Equations**

V(z,t)= f

^{+}(t-z/v

_{p}) + f

^{-}(t+z/v

_{p}) [1] where f is some arbitrary function.

∂V/∂z= -L(∂I/∂t) [2]

∂I/∂z= -C(∂V/∂t) [3]

**3. The Attempt at a Solution**

Ok,so I tried starting with [3] and integrating with respect to time: ∫(∂I/∂z)∂t= ∫(-C(∂V/∂t))∂t

which gives (I think) V=-1/C ∫(∂I/∂z)∂t

now differentiating this with respect to z: ∂V/∂z= ∂/∂z[-1/C ∫(∂I/∂z)∂t]

and substituting the RHS of this in to [2]:∂/∂z[-1/C ∫(∂I/∂z)∂t]=-L(∂I/∂t)

now I'm stuck and not sure where to go from here. The solution is the well known equation

I(z,t)= (1/Z

_{0})[f

^{+}(t-z/v

_{p}) + f

^{-}(t+z/v

_{p})] where Z

_{0}=√(L/C)

I would appreciate knowing the steps to get there.

Thanks very much