Question

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

Answer 1

Answer on Question #74747 Physics / Other

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

Solution:

The time constant

$$\tau = RC = 22 \times 10^{-3} \times 2 \times 10^{-6} = 44 \times 10^{-9}\,\mathrm{s} = 44\,\mathrm{ns}.$$

The potential difference across the capacitor

$$V(t) = V e^{-t / \tau}$$

So

$$V(\tau) = V e^{-1} = 60 e^{-1} = 22\,\mathrm{V}.$$

**Answers:** 44 ns, 22 V

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