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Capacitor question

2023 · 1 Feb · Shift 2 · Q52
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  5. /2023 · 1 Feb · Shift 2 · Q52

Capacitor question

2023 · 1 Feb · Shift 2 · Q52

JEE MainPhysicsCapacitorMCQ+4 / −1
Given below are two statements: One is labeled as Assertion A and the other is labeled as Reason R. Assertion A : Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason R : Capacitance of metallic spheres depend on the radii of spheres In light of the above statements, choose the correct answer from the options given below.
  1. A
    Both A\mathbf{A}A and R\mathbf{R}R are true but R\mathbf{R}R is not the correct explanation of A\mathbf{A}A
  2. B
    Both A\mathbf{A}A and R\mathbf{R}R are true and R\mathbf{R}R is the correct explanation of A\mathbf{A}A
  3. C
    A\mathbf{A}A is false but R\mathbf{R}R is true
  4. D
    A\mathbf{A}A is true but R\mathbf{R}R is false
View written solutionFree

Correct answer: C

  1. Use the relation between charge, potential, and capacitance

For any isolated conductor, Q=CVQ = CVQ=CV where QQQ is charge, CCC is capacitance, and VVV is potential.

  1. Capacitance of a metallic sphere

For an isolated metallic sphere of radius RRR, C=4πε0RC = 4\pi \varepsilon_0 RC=4πε0​R This depends only on the radius of the sphere, not on whether the sphere is solid or hollow.

  1. Check Assertion A

Both spheres are at the same potential and have the same radius.

So their capacitances are equal: Csolid=Chollow=4πε0RC_{\text{solid}} = C_{\text{hollow}} = 4\pi\varepsilon_0 RCsolid​=Chollow​=4πε0​R

Since Q=CVQ=CVQ=CV and both have the same CCC and same VVV, Qsolid=QhollowQ_{\text{solid}} = Q_{\text{hollow}}Qsolid​=Qhollow​

Therefore, the statement

"Solid sphere will have lower charge than the hollow one"

is false.

  1. Check Reason R

The reason says:

"Capacitance of metallic spheres depend on the radii of spheres"

This is true, because C=4πε0RC = 4\pi \varepsilon_0 RC=4πε0​R

  1. Choose the correct option
  • Assertion A: False
  • Reason R: True

Hence the correct option is: C\boxed{\text{C}}C​

  1. Compare with stored correct answer

Stored correct answer: C\text{C}C

This matches my derived answer.

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