Question 143: Electrostatics & Capacitance

Question

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $${x \over {15}}{{{ \in _0}A} \over b}$$. The value of x is ____________.

Accepted Answer

The circuit is equivalent to 3 capacitors in parallel as shown
$${C_{eq}} = {{{\varepsilon _0}A} \over b}\left( {1 + {1 \over 3} + {1 \over 5}} \right) = {{23} \over {15}}{{{\varepsilon _0}A} \over b}$$
$$ \Rightarrow x = 23$$

Electrostatics & Capacitance

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is ${x \over {15}}{{{ \in _0}A} \over b}$. The value of x is ____________.

Integer / Numeric Answer Type