A controller on an electronic arcade game consists of a variable resistor connec

Question

A controller on an electronic arcade game consists of a variable resistor connected across the plates of a 0.330 ?F capacitor. The capacitor is charged to 5.50 V, then discharged through the resistor. The time for the potential difference across the plates to decrease to 0.800 V is measured by a clock inside the game. If the range of discharge times that can be handled effectively is from 10.0?s to 4.00 ms, what should be the lower value of the resistance range of the resistor? b) And what should be the higher value of the resistance range of the resistor?

Explanation / Answer

We have

V = 5.5 e^ -t/RC

0.8/5.5 = e^-t/RC

1.92 = t/RC

R = t/ 1.92 C

Now 10 uS < t < 4 mS

So 15.78 < t/1.92*0.33 *10^-6 < 6313.13

So 15.78 ohms < R < 6.313 Kilo ohms

a) lower value = 15.78 ohms

b) higher value = 6.313 kilo ohms

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