   Chapter 18, Problem 54AP

Chapter
Section
Textbook Problem

The resistance between points a and b in Figure P18.54 drops to one-half its original value when switch S is closed. Determine the value of R. Figure P18.54

To determine
The time required for the charge on the capacitor to reach 90%.

Explanation

Given Info: The resistor is R=2.0×106Ω and the capacitance of the circuit is C=3.0μF

Explanation:

Formula to calculate the time constant of the RC circuit is,

τ=RC

• τ is the time constant,
• R is the resistor,
• C is the capacitance,

Substitute 2.0×106Ω for R and 3.0μF for C .

τ=(2.0×106Ω)(3.0μF)(106F1μF)=6.0s

Thus, the time constant of the RC circuit is 6.0 s.

Conclusion:

Formula for the charge on the capacitor at a time t is,

q=Qmax(1et/τ) (1)

• q is the charge on the capacitor,
• Qmax is the maximum charge stored in the capacitor to reach 90% of its final value,
• t is the time required to stored maximum charge,

Formula for the maximum charge on the capacitor o reach 90% of its final value is,

q=0

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