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)

Correct Answer: C

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, \[C=4\pi {{\varepsilon }_{0}}R\]