Question

(a) Calculate the capacitance needed to get an \(RC\) time constant of \(1.00 \times {10^3}\;s\) with a \(0.100 - \Omega \) resistor. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

Short answer

1. Capacity is \(10000\;F\).
2. If we know that the earth's capacity is finite, the capacity required is irrational.

Step-by-step solution

Definition of RC constant and resistance.

RC time constant: This measurement informs us how long it will take a cap to charge to a particular voltage level.

Anything that prevents current flow is referred to as "resistance" in this context.

Given Information.

• \(RC\)time constant is:\(1.00 \times {10^3}{\rm{ }}s\)
• Resistor: \(0.100 - \Omega \).

Calculate the capacity needed.

a)

We can calculate the capacity needed to have a time constant of\({10^3}\;s\):

\(\begin{aligned}{c}C = \frac{\tau }{R} = \frac{{{{10}^3}}}{{0.1}}\\C = 10000\;F\end{aligned}\)

Hence, Capacity is \(10000\;F\).

Explanation of solution.

(b)

Unreasonable is the capacity needed if we know that earth's capacity is \(1F\).