diff --git a/_psets/5.md b/_psets/5.md index c8792a42eb5d42960d7d8096057e478ad4c03e5d..80d653ece8759db8e814a39bc48f2803203ee49a 100644 --- a/_psets/5.md +++ b/_psets/5.md @@ -172,7 +172,10 @@ mil is a thousandth of an inch), what is the inner diameter? Solving the formula above for $$r_i$$, $$ -r_i = r_0 \cdot e^{-2 \pi \cdot 51.6 \sqrt{\epsilon_0 \epsilon_r / \mu_0}} +\begin{align*} +r_i &= r_0 \cdot e^{-2 \pi \cdot 51.6 \sqrt{\epsilon_0 \epsilon_r / \mu_0}} \\ +&= 8.2 \si{mils} +\end{align*} $$ ### (e) @@ -181,10 +184,12 @@ $$ For RG58/U, at what frequency does the wavelength become comparable to the diameter? -We know $$\lambda \nu = c$$, so - $$ -\num{2e8} \si{m/s} \cdot \frac{1}{2 \cdot \num{1.48e-3} \si{m}} = \num{6.76e10} \si{Hz} +\begin{align*} +\nu &= \frac{c}{\lambda} \\ +&= \frac{\num{2e8} \si{m/s}}{2 \cdot \num{1.48e-3} \si{m}} \\ +&= \num{6.76e10} \si{Hz} +\end{align*} $$