Question

Two conducting spheres of radii R1 and R2 are kept widely separated from each other. What are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series−parallel connections.

Answer 1

Answer:

sorry i don't know the answer

Answer 2

The total capacitance of the combination circuit is given by $C=$  $4 \pi \in_{0}\left(R_{1}+R_{2}\right)$

Explanation:

Step 1:

We know that Charge $Q=C X V$

Where Q = Charge

C = Capacitance

V = Voltage in the circuit

Step 2:

From the equation we re-write the equation

Capacitance $\mathrm{c}=\mathrm{Q} / \mathrm{v}$

$C=\frac{q}{V}, \text { Now } V=\frac{K q}{R}$

$\text { So, } C_{1}=\frac{q}{\left(\mathrm{Kq} / \mathrm{R}_{1}\right)}=\frac{\mathrm{R}_{1}}{\mathrm{K}}=4 \pi \varepsilon_{0} \mathrm{R}_{1}$

similarly $c_{2}=4 \pi \varepsilon_{0} R_{2}$

Step 3:

From the above equation we can say that equivalent capacitance  

$\mathrm{Ceq}=4 \pi \in \mathrm{OR} 1+4 \pi € \mathrm{OR} 2$

      =$4 \pi \in 0(\mathrm{R} 1+\mathrm{R} 2)$

Therefore, the total capacitance of the combination circuit is given by$=4 \pi \epsilon 0(\mathrm{R} 1+\mathrm{R} 2)$