\begin{problem*}{19.7} % resistor networks
A $650\U{\Ohm}$ and a $2200\U{\Ohm}$ resistor are connected in series
with a $12\U{V}$ battery.  What is the voltage across the
$2200\U{\Ohm0}$ resistor?
\end{problem*}

\begin{solution}
First we find the total current in the circuit.  The two resistances,
$R_1 = 650\U{\Ohm}$ and $R_2 = 2200\U{\Ohm}$, in series provide an
effective resistance of $R_e = R_1 + R_2$.  By Kirchhoff's loop rule
\begin{align*}
  V - I R_e &= 0 \\
  I &= \frac{V}{R_e} = \frac{V}{R_1 + R_2}
\end{align*}
And applying Ohm's law to the second resistor
\begin{align*}
  V_2 = I R_2 = \frac{V R_2}{R_1 + R_2} = \ans{9.3\U{V}}
\end{align*}
\end{solution}
