• # question_answer For a capacitor Q = CV, so choose the correct option. A)  Q is the net charge on the capacitor              B)  C depends on Q and V C)  C do not depend on Q D)  V is the potential of a single plate of the capacitor (if we assuming parallel plate capacitor)

Solution :

Idea Let us consider a parallel plate capacitor In Q = CV, Q is the charge on a single plate of the capacitor. ${{Q}_{net}}$on the capacitor is zero. The capacitance is an intrinsic property of the capacitor, it does not depend on Q and V. Here V is potential difference. Net charge on a capacitor$=+Q-Q=0$and C neither depend on Q nor on V. It is an intrinsic characteristic of a capacitor. For parallel plate capacitor, C$=\frac{{{\varepsilon }_{0}}A}{d}$ Here, V is not potential, it is potential difference between the plates of the capacitor. TEST Edge Consider an isolated conducting sphere having charge. $\Rightarrow$ ${{V}_{\text{Surface}}}=\frac{Q}{4\pi {{\varepsilon }_{0}}r}$and ${{V}_{\text{infinity}}}=0$ $\Rightarrow$ $\Delta V=\frac{Q}{4\pi {{\varepsilon }_{0}}r}$ $\Rightarrow$$\Delta V={{V}_{\text{Surface}}}-{{V}_{\text{infinity}}}=\frac{Q}{4\pi {{\varepsilon }_{0}}r}$ $\Rightarrow$$\Delta V={{V}_{\text{Surface}}}=\frac{Q}{4\pi {{\varepsilon }_{0.}}r}$ $\Rightarrow$$Q=4\pi {{\varepsilon }_{0}}R{{V}_{\text{Surface}}}=4\pi {{\varepsilon }_{0}}R\Delta V$ $\Rightarrow$So, $C=4\pi {{\varepsilon }_{0}}R$

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