Question

A 2UF capacitor charged originally to a potential difference of 60v is
discharged across a 22mΩ resistor as shown in the figure. Calculate
the time constant of the circuit and the potential difference across the
capacitor after this time constant time?

Answer 1

Answer on Question #74366 Physics / Other

A $C = 2\mu \mathrm{F}$ capacitor charged originally to a potential difference of $V_{0} = 60\mathrm{V}$ is discharged across a $R = 22\mathrm{m}\Omega$ resistor as shown in the figure. Calculate the time constant of the circuit and the potential difference across the capacitor after this time constant time?

Solution:

The time constant

$$\tau = R C = 2 2 \times 1 0 ^ {- 3} \times 2 \times 1 0 ^ {- 6} = 4 4 \times 1 0 ^ {- 9} \mathrm {s}$$

The potential difference across the capacitor as a function of time

$$V (t) = V _ {0} e ^ {- \frac {t}{\tau}}$$

So

$$V (\tau) = V _ {0} e ^ {- 1} = 6 0 \times e ^ {- 1} = 2 2 \mathrm {V}$$

Answers: $44 \times 10^{-9} \mathrm{~s}, 22 \mathrm{~V}$

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