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The capacitance of a parallel plate capacitor formed by circular plates of diameter 4.0 cm is equal to the capacitance of a sphere of diameter 200 cm. Find the distance between the two plates.

Asked in RS Academy GUJCET booklet · Capacitance of a conductor and a capacitor

• (1) 2×10⁻⁴ m
• (2) 1×10⁻⁴ m
• (3) 3×10⁻⁴ m
• (4) 4×10⁻⁴ m

Step-by-step solution

Why the other options are wrong

• (1) Uses both diameters as radii — 4 cm for the plates and 2 m for the sphere: ((0.04)²)/(4×2)=2×10⁻⁴ m.
• (3) No single slip gives 3×10⁻⁴ m. Sanity check: d=(r²)/(4R)=((0.02)²)/(4×1)=1×10⁻⁴ m.
• (4) Uses the plate diameter as its radius: ((0.04)²)/(4×1)=4×10⁻⁴ m. The plate radius is 2 cm.

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