A) \[{{R}^{2}}\]
B) \[\frac{1}{{{R}^{2}}}\]
C) \[\frac{1}{{{R}^{4}}}\]
D) R
Correct Answer: D
Solution :
On going a charge q to a conductor, the electric potential of the conductor becomes V. Then, the capacitance of the conductor is \[C=\frac{q}{V}\] Potential on sphere of radius R is given by \[V=\frac{1}{4\pi {{\varepsilon }_{0}}}\,\frac{q}{R}\,V.\] \[\therefore \] \[C=\frac{q\times 4\pi {{\varepsilon }_{0}}R}{q}=4\pi {{\varepsilon }_{0}}R\] \[\Rightarrow \] \[C\propto R\]
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