Question

Derive an expression for the effective capacitance when capacitors are connected

Answer 1

when capacitor are connected in series the charge remains constant and voltage changes$,$ so

$$V = {V_1} + {V_2} + {V_3}$

We know that

$C=\frac{Q}{V}$

$\Rightarrow V=\frac{Q}{C}$

$\frac{Q}{C_{eff}}=\frac{Q}{C_1}+\frac{Q}{C_2}+\frac{Q}{C_3}$

$\frac{1}{C_{eff}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$

Capacitor is parallel$:$

When capacitor are connected in parallel charge varies but voltage remains constant i

$C_{eff}V=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$

$\Rightarrow C_{eff}=C_1+C_2+C_3$