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Question: A capacitor made of two circular plates each of radius 12 cm and separated by 5mm. The capacitor is ...

A capacitor made of two circular plates each of radius 12 cm and separated by 5mm. The capacitor is being charged by an external source. The charging current is constant and equal to 0.15 A. The capacitance of the parallel plate capacitor is

A

40 Pf

B

45 pF

C

70 pF

D

80 pF

Answer

80 pF

Explanation

Solution

: Here, R=12cm=0.12mR = 12cm = 0.12m

d=5mm=5×10−3md = 5mm = 5 \times 10^{- 3}m

ε0=8.85×10−12C2N−1m−2\varepsilon_{0} = 8.85 \times 10^{- 12}C^{2}N^{- 1}m^{- 2}

Also, A=πR2=3.14×(0.12)2m2A = \pi R^{2} = 3.14 \times (0.12)^{2}m^{2}

=4.5×10−2m2= 4.5 \times 10^{- 2}m^{2}

Capacitance,C=ε0AdC = \frac{\varepsilon_{0}A}{d}

=8.85×10−12×4.5×10−25×10−3= \frac{8.85 \times 10^{- 12} \times 4.5 \times 10^{- 2}}{5 \times 10^{- 3}}

=79.65×10−12=80pF= 79.65 \times 10^{- 12} = 80pF