The capacitor of capacitance $C$ in the circuit shown is fully charged initially, Resistance is $R$.

After the switch $S$ is closed, the time taken to reduce the stored energy in the capacitor to half its initial value is: 

An electron enters a parallel plate capacitor with horizontal speed $\mu$ and is found to deflect by angle $\theta$ on leaving the capacitor as shown. It is found that $\tan \theta =0.4$ and gravity is negligible.

If the initial horizontal speed is doubled, then $\tan \theta$ will be:

Two identical parallel plate capacitors of capacitance $C$ each are connected in series with a battery of emf $E$ as shown. If one of the capacitors is now filled with a dielectric of dielectric constant $k$, the amount of charge which will flow through the battery is (neglect internal resistance of the battery),

What are the charges stored in the $1 \mathrm{\mu }\text{F}$ and $2 \mathrm{\mu }\text{F}$ capacitors in the circuit below, once the currents become steady