Question

A capacitor is made of a flat plate of area A and a second plate having a stair like structure as shown in diagram. The capacitance of the arrangement is-

• A. $\frac { \varepsilon _ { 0 } \mathrm {~A} } { \mathrm {~d} }$
• B. $\frac { 18 } { 11 } \frac { \varepsilon _ { 0 } \mathrm {~A} } { \mathrm {~d} }$
• C. $\frac { 11 } { 18 } \frac { \varepsilon _ { 0 } \mathrm {~A} } { \mathrm {~d} }$
• D. $\frac { \varepsilon _ { 0 } \mathrm {~A} } { 3 \mathrm {~d} }$

Answer 1

Answer: (C)

$\frac { 11 } { 18 } \frac { \varepsilon _ { 0 } \mathrm {~A} } { \mathrm {~d} }$

Answer 2

C_eq = C₁ + C₂ + C₃

= $\frac { \varepsilon _ { 0 } \mathrm {~A} } { 3 \mathrm {~d} }$ + $\frac { \varepsilon _ { 0 } \mathrm {~A} } { 3 \mathrm {~d} \times 2 }$ = $\frac { \varepsilon _ { 0 } \mathrm {~A} } { 3 \times 3 \mathrm {~d} }$ = $\frac { 11 \varepsilon _ { 0 } \mathrm {~A} } { 18 \mathrm {~d} }$