Question

The outer cylinders of two cylindrical capacitors of capacitance $2.2\mu F$ each , are kept in contact and the inner cylinder are connected through a wire. A battery of emf $10V$ is connected as shown in figure. Find the total charge supplied by the battery to the inner cylinders.

Answer 1

$\text{Step 1: Simplify and Redraw the circuit}$

The Inner cylinders of the capacitors are connected to the $+ve$ terminal of the battery(Point $A$) and outer cylinders are connected to the $-ve$ terminal of the battery(Point $B$).

They both together make two capacitors in parallel say $C_1$ and $C_2$ as shown in the figure.

$\text{Step 2: Calculation of equivalent capacitance by combining series or parallel capacitors}$

The Capacitors are in parallel combination.

$\therefore C_{eq}=C_1+C_2=2.2\mu F+2.2\mu F=4.4\mu F$

$\text{Step 3: Total Charge supplied by the battery}$

The total charge supplied by the battery to the inner cylinders is given by:

$Q=C_{eq}V=4.4\mu F\times 10V=44\mu C$