Concept Simulation 20.4 provides background for this problem and gives you the opportunity to verify your answer graphically. How many time constants (a decimal number) must elapse before a capacitor in a series RC circuit is charged to 83.0% of its equilibrium charge?

The number of time constants is

Explanation:

Let us denote the equilibrium charge with

    From the question we are told that

       for the duration we are to obtain the final charge on the capacitor should be 83% of

Generally in an RC circuit an equation that defines charge after a time t is  mathematically represented as

Where q is the final charge = 83%  = 0.83

           RC is the time constant

Substituting values

    Taking natural log of both sides

=>        

Since RC is the time constant then the number of time constant is

The time constant is 1.772

Explanation:

Given that,

Charge,  

We need to calculate the time constant

Using expression for charging in a RC circuit

Where, = time constant

Put the value into the formula

Thus, The time constant is 1.772