(Solved): 1. Consider the circuit drawn to the right. A) Label the charge Q4, Q2 and Q1.5 on the 3 capacitors ...

1. Consider the circuit drawn to the right. A) Label the charge Q4, Q2 and Q1.5 on the 3 capacitors. How are they related to each other just considering charge conservation? B) What is the equivalent capacitance for the circuit? Note that the voltage across two resistors in parallel are the same. Therefore voltage drop across two resistors in series is not the same but must add to each other. C) How much charge flows through the battery to fully charge the capacitors in the circuit? D) What is the voltage drop across the 1.5 microf capacitor? E) What is the charge on the 1.5 microf capacitor? 2. Consider the circuit to the right with a switch that can be set to connect either point $A$ or point $B$ or neither. Let the battery voltage be $\mathrm{Vb}$. Assume that the switch is in the all off position shown for a very long time. a) At time $=0$, the switch connects to point $A$. What happens to the Capacitor, in words? b) What is the functional form of the charge $Q(t)$ on the positive (upper) plate of the capacitor. Draw this shape on a plot of $Q(t)$ vs $t$. c) Find the functional form of $I(t)$ from direct differentiation of $Q(t)$, ie., $l=dQ/dt$. d) What is the peak current at time $=0$. Note that it is when the slope of $Q$ is the highest at $t=0$. e) At some later time $t1$, the switch is moved to connect point $B$. What happens to the charge on the capacitor after time $t>t$ ? What is this called? f) What is the functional form of $Q(t)$ starting from $Q(t1)$ for $t>1$. g) Is the RC constant the same while connected to $A$ and to $B$ ? h) What is the direction of current flow when connected to the battery and $A$ and when the switch is connected to $B$. i) Sketch the full $Q(t)$ for $t>0$ and after $t1=\left(R{1}^{?}C\right)$ assuming $R2=3R1$.