Electric Circuits

Two capacitors, with capacitances of 3 $\mu$F and 6 $\mu$F, are connected in series. What is the equivalent capacitance of this combination?

Three capacitors, with capacitances of 2 $\mu$F, 4 $\mu$F and 6 $\mu$F, are connected in parallel. What is the equivalent capacitance of this combination?

A circuit contains a 4 $\mu$F capacitor in series with a parallel combination of a 3 $\mu$F and a 6 $\mu$F capacitor. What is the equivalent capacitance of the entire combination?

A 2 $\mu$F and a 6 $\mu$F capacitor are connected in series to a 16 V battery. Find the charge on the 2 $\mu$F capacitor.

An RC circuit has a resistance of 200 $\Omega$ and a capacitance of 50 $\mu$F. What is the time constant of this circuit?

In an RC circuit, what value of resistance is needed with a 20 $\mu$F capacitor to achieve a time constant of 0.004 s?

How does increasing the capacitance and decreasing the resistance in an RC circuit affect the time it takes for the capacitor to charge to 50% of its maximum charge?

In an RC charging circuit with a voltage of 12V and a resistance of 100 $\Omega$, what is the initial current immediately after the switch is closed?

In an RC charging circuit, what is the approximate charge on the capacitor after a time equal to one time constant ($\tau$)?

In a charging RC circuit, derive an expression for the voltage across the capacitor as a function of time, given an electromotive force $\mathcal{E}$, resistance $R$, and capacitance $C$.