Chapter 16 - Electric Potential, Energy, and Capacitance - Learning Path Questions and Exercises - Conceptual Questions - Page 591: 24

a). If they are in series, $\frac{1}{C_{s}}=\frac{1}{C}+\frac{1}{C}+.......... N \,\,times=\frac{N}{C}$ Thus, $C_{s}=\frac{C}{N}$ b). If they are connected in parallel, $C_{p}=C+C+............ N\,\, times=NC$ c). Here if $C_{s}$ is equivalent of half of the capacitors, then $\frac{1}{C_{s}}=\frac{1}{C}+\frac{1}{C}+........ \frac{N}{2}\,\, times=\frac{N}{2C}$ Thus, $C_{s}=\frac{2C}{N}$ Hence, total equivalent = $C_{p}=C_{s}+C_{s}=\frac{4C}{N}$

a). If they are in series, $\frac{1}{C_{s}}=\frac{1}{C}+\frac{1}{C}+.......... N \,\,times=\frac{N}{C}$ Thus, $C_{s}=\frac{C}{N}$ b). If they are connected in parallel, $C_{p}=C+C+............ N\,\, times=NC$ c). Here if $C_{s}$ is equivalent of half of the capacitors, then $\frac{1}{C_{s}}=\frac{1}{C}+\frac{1}{C}+........ \frac{N}{2}\,\, times=\frac{N}{2C}$ Thus, $C_{s}=\frac{2C}{N}$ Hence, total equivalent = $C_{p}=C_{s}+C_{s}=\frac{4C}{N}$