Spherical Conductor Capacitance – Rankers Physics

Spherical Capacitors: Practice Problem & Solution

Assertion (A): It is not possible to make a spherical conductor of capacitor one farad. Reason (R): It is possible for earth as its radius is \( 6400 \text{ km} \).  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Spherical Capacitors. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is true. For an isolated sphere, \( C = 4\pi \epsilon_0 R ). For \( C=1 \text{ F} \), \( R \approx 9 \times 10^9 \text{ m} \), which is astronomically large. Reason (R) is false. Earth's capacitance is \( C \approx 711 \mu\text{F} ), far less than 1 Farad.

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