## A capacitor in a single-loop RC circuit is charged to 85% of its final potential difference in 2.4 s. What is the time constant for this cir

Question

A capacitor in a single-loop RC circuit is charged to 85% of its final potential difference in 2.4 s. What is the time constant for this circuit

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1 year 2021-08-15T03:46:19+00:00 1 Answers 143 views 0

The  time constant is  $$\tau = 1.265 s$$

Explanation:

From the question we are told that

the time take to charge is  $$t = 2.4 \ s$$

The mathematically representation for voltage potential of a capacitor at different time is

$$V = V_o – e^{-\frac{t}{\tau} }$$

Where  $$\tau$$  is the time constant

$$V_o$$ is the potential of the capacitor when it is full

So  the capacitor potential will be  100%  when it is full thus  $$V_o =$$100%  =  1

and from the  question we are told that the  at the given time the potential of the capacitor is 85% = 0.85 of its final potential so

V  = 0.85

Hence

$$0.85 = 1 – e^{-\frac{2.4}{\tau } }$$

$$- {\frac{2.4}{\tau } } = ln0.15$$

$$\tau = 1.265 s$$