Question

Rank in order, from largest to smallest, the potential differences ${(∆V_C)}_1\mathrm{to}{(∆V_C)}_4$of the four capacitors in Figure Q26.12. Explain.

Short answer

The potential differences are :${\mathbf{(}\mathbf{∆}{\mathbf{V}}_{\mathbf{c}}\mathbf{)}}_{\mathbf{3}}\mathbf{>}{\mathbf{(}\mathbf{∆}{\mathbf{V}}_{\mathbf{c}}\mathbf{)}}_{\mathbf{4}}\mathbf{=}{\mathbf{(}\mathbf{∆}{\mathbf{V}}_{\mathbf{c}}\mathbf{)}}_{\mathbf{1}}\mathbf{>}{\mathbf{(}\mathbf{∆}{\mathbf{V}}_{\mathbf{c}}\mathbf{)}}_{\mathbf{2}}$

Step-by-step solution

: Given information and formula used   

Given Figure :

Formula used :

$∆V_c=\frac{Q}{C}$

Calculating the potential differences 

Calculating each capacitor's $∆V_c=\frac{Q}{C}$

$\Rightarrow {(∆V_c)}_1=\frac{Q}{C},{(∆V_c)}_2={0.5(∆V_c)}_1$

${(∆V_c)}_3={2(∆V_c)}_1,{(∆V_c)}_4={(∆V_c)}_1$

So,${\mathbf{(}\mathbf{∆}{\mathbf{V}}_{\mathbf{c}}\mathbf{)}}_{\mathbf{3}}\mathbf{>}{\mathbf{(}\mathbf{∆}{\mathbf{V}}_{\mathbf{c}}\mathbf{)}}_{\mathbf{4}}\mathbf{=}{\mathbf{(}\mathbf{∆}{\mathbf{V}}_{\mathbf{c}}\mathbf{)}}_{\mathbf{1}}\mathbf{>}{\mathbf{(}\mathbf{∆}{\mathbf{V}}_{\mathbf{c}}\mathbf{)}}_{\mathbf{2}}$