A parallel-plate capacitor with plate area $20 c m^{2}$ and plate separation $1.0 m m$ is connected to a battery. The resistance of the circuit is $10 k Ω$ . Find the time constant of the circuit.

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Solution

$A = 20 c m^{2} = 20 \times 106 - 4 m^{2}$
$d = 1 m m = 1 \times 10^{- 3} m; R = 10 k Ω$
$C = \frac{E_{0} A}{d} = \frac{8.85 \times 10^{- 12} \times 20 \times 10^{- 4}}{1 \times 10^{- 3}}$

$= \frac{8.85 \times 10^{- 12} \times 2 \times 10^{- 3}}{10^{- 3}} = 17.7 \times 10^{- 2}$ Farad.

Time constant $= C R = 17.7 \times 10^{- 2} \times 10 \times 10^{3}$
$= 17.7 \times 10^{- 8} = 0.177 \times 10^{- 8} s = 0.18 μ s$ .

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A parallel-plate capacitor with plate area 20cm2 and plate separation 1.0mm is connected to a battery. The resistance of the circuit is 10kΩ. Find the time constant of the circuit.

A=20cm2=20×106−4m2d=1mm=1×10−3m;R=10kΩC=E0Ad=8.85×10−12×20×10−41×10−3=8.85×10−12×2×10−310−3=17.7×10−2 Farad.Time constant =CR=17.7×10−2×10×103=17.7×10−8=0.177×10−8s=0.18μs.

A parallel-plate capacitor with plate area $20 c m^{2}$ and plate separation $1.0 m m$ is connected to a battery. The resistance of the circuit is $10 k Ω$ . Find the time constant of the circuit.