Questions:

1. The voltage across $R_2$ of a voltage divider is some fraction of the battery voltage. Can you express this fraction in a simple English sentence?
2. Show using Kirchhoff's Laws what that
   
   $$V_2 = V_b \frac{R_2}{R_1 + R_2},$$
   
   
   for a voltage divider comprising a DC battery of voltage $V_b$ in series with resistances $R_1$ and $R_2$.
3. Do some research and give an example of an electrical device which is essentially a voltage divider.
4. Show that for a capacitor $C$ in series with a resistance $R$ in series with a battery $V_b$ that the time for the voltage across the capacitor to reach 1/2 of its final value is $\tau \ln{2}$.