What multiple of the time constant $\tau$ gives the time taken by an initially uncharged capacitor in an $RC$ series circuit to be charged to $89.0\%$ of its final charge?

In figure an array of $n$ parallel resistors is connected in series to a resistor and an ideal battery. All the resistors have the same resistance. If an identical resistor were added in parallel to the parallel array, the current through the battery would change by $0.833\%.$ What is the value of $n$?

In the following figure, the resistances are $R_1=3.00 \mathrm{\Omega }, R_2=7.00 \mathrm{\Omega }$ and the battery is ideal. What value of $R_3$ maximizes the dissipation rate in resistance $3$?

A capacitor with an initial potential difference of $80.0 \mathrm{V}$ is discharged through a resistor when a switch between them is closed at $t=0.$ At $t=10.0 \mathrm{s},$ the potential difference across the capacitor is $1.00 \mathrm{V}$ . (a) What is the time constant of the circuit? (b) What is the potential difference across the capacitor at $t=17.0 \mathrm{s}?$

In the following figure, the current in resistance $6$ is $i_6=2.80 \mathrm{A}$ and the resistances are $R_1=R_2=R_3=2.00 \mathrm{\Omega }, R_4=16.0 \mathrm{\Omega }, R_5=8.00 \mathrm{\Omega }$ and $R_6=4.00 \mathrm{\Omega }.$  What is the emf of the ideal battery?

In the following figure, ${\epsilon }_1=8.00 \mathrm{V}$, ${\epsilon }_2=12.0 \mathrm{V}, R_1=100 \mathrm{\Omega }, R_2=200 \mathrm{\Omega }$ and $R_3=300 \mathrm{\Omega }$ . One point of the circuit is grounded $(V=0).$ What are the (a) size and
(b) direction (up or down) of the current through resistance $1,$ the (c) size and (d) direction (left or right) of the current through resistance $2,$ and the (e) size and (f) direction of the current through resistance $3 ?$ (g) What is the electric potential at point $A$?

Switch S in the following figure is closed at time $t=0,$ to begin charging an initially uncharged capacitor of capacitance $C=49.0 \mu \mathrm{F}$ through a resistor of resistance $R=32.0 \mathrm{\Omega }$ . At what time is the potential across the capacitor equal to that across the resistor?

A simple ohmmeter is made by connecting a $9.00 \mathrm{V}$ flashlight battery in series with a resistance $R$ and an ammeter that reads from $0$ to $1.00 \mathrm{mA}$, as shown in the figure. Resistance $R$ is adjusted so that when the clip leads are shorted together, the meter deflects to its full-scale value of $1.00 \mathrm{mA}$, what external resistance across the leads results in a deflection of 

(a) $10.0\%$ 

(b)$50.0 \%,$

(c) $90.0\%$ of full scale? 

(d) If the ammeter has a resistance of $20.0 \mathrm{\Omega }$ and the internal resistance of the battery is negligible, what is the value of $R ?$