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In a parallel plate capacitor, the area of each plate is A=1 m² and the distance between the two plates is d=1 mm. Then the capacitance of the capacitor is C= ______ F.

Asked in GSEB Board July 2021 · Capacitance of a conductor and a capacitor

• (1) 8.85×10⁻¹²
• (2) 8.85×10⁻⁹
• (3) 8.85×10⁻⁶
• (4) 8.85×10⁻¹⁵

Step-by-step solution

Why the other options are wrong

• (1) Leaves the separation out, as if d were 1 m: that is just ε₀×1. Dividing by d=10⁻³ m raises it a thousandfold.
• (3) Converts 1 mm with the area factor 10⁻⁶ — that is 1 mm² in square metres. A length of 1 mm is 10⁻³ m.
• (4) Multiplies by d instead of dividing: 8.85×10⁻¹²×10⁻³. Capacitance grows as the plates come closer, so d belongs in the denominator.

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