Chapter 27, Problem 083 A controller on an electronic arcade game consists of a

Question

Chapter 27, Problem 083 A controller on an electronic arcade game consists of a variable resistor connected across the plates of a 0.251 F capacitor. The capacitor is charged to 5.00 V, then discharged through the resistor. The time for the potential difference across the plates to decrease to 0.830 V is measured by a clock inside the game. If the range of discharge times that can be handled effectively is from 12.3 s to 6.11 ms, what should be the (a) lower value and (b) higher value of the resistance range of the resistor? (a) Number (b) Number Show Work is REQUIRED for this question: Units Units Open Show Work

Explanation / Answer

Given,

V0 = 5 V

Capacitance, C = 0.251 uF

V = 5 x e^(-t/RC)

(t/RC) = ln(5/0.83)

==> R = t/(1.80 C)

for lower value of range of resistance t is lower

Resistance, R = 12.3/(1.80 x 0.251) = 27.29 ohms

B)

Lower value of range of resistance t is higher

Resistance, R = (6.11 x 10^-3)/(1.80 x 0.251 x 10^-6) = 13523.68 ohms

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