Question

The graph shows the variation of voltage (v) across the plates of two parallel plate capacitors $A$ and $B$ versus increase of charge $Q$ stored in them. Then

• A. capacity of both capacitors is same.
• B. capacity of $A$ is higher than $B$.
• C. capacity of $B$ is higher than $A$.
• D. capacity of both is zero.

Hint:

In a \(V\)-vs-\(Q\) graph: \[ \text{slope}=\frac{1}{C} \] So smaller slope means larger capacitance.

Answer 1

The Correct Option is C

Concept:
For a capacitor: \[ Q=CV \quad \Rightarrow \quad V=\frac{Q}{C} \] So in a graph of \(V\) versus \(Q\), slope is: \[ \frac{V}{Q}=\frac{1}{C} \] ip

Step 1: Relate slope with capacitance.
Higher slope means: \[ \frac{1}{C}\text{ is higher} \] so capacitance is lower. Lower slope means capacitance is higher. ip

Step 2: Interpret the graph.
From the graph, capacitor \(A\) has steeper line and capacitor \(B\) has smaller slope. Therefore: \[ C_B > C_A \] ip Hence, the correct answer is:
\[ \boxed{(C)\ \text{capacity of }B\text{ is higher than }A} \]