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 39.0% of its equilibrium charge

t = 0.492τ

Explanation: In a circuit where there is a resistor and a capacitor, the equation for a charging capacitor is given by:

where:

is the equilibrium charge

q is the charge at time t

RC is time constant also called τ (tau)

For this problem, the circuit is charged to 39%, which means: q =

0.39 = 1 -

= 0.61

= ln(0.61)

-t = ln(0.61)τ

t = 0.492τ

For the condition to be met it is needed 0.492 time constants must elapse.

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