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The distance between the two plates of a parallel plate capacitor is doubled and the area of each plate is halved. If C is its initial capacitance, its final capacitance is equal to:
Asked in Re-NEET 2022 · Capacitance of a conductor and a capacitor
- (1) C/4
- (2) 2C
- (3) C/2
- (4) 4C
Answer: (1) C/4
Step-by-step solution
C=(ε₀A)/d.
C'=(ε₀(A/2))/(2d)=C/4.
Why the other options are wrong
- (2) Treats C as proportional to d and inversely to A; it is the other way round, C=(ε₀A)/d.
- (3) Applies only one of the two changes; both the smaller area and the wider gap reduce the capacitance.
- (4) Inverts both dependences: C=(ε₀A)/d falls when A falls and when d rises.
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