A controller on an electronic arcade game consists of a variable resistor connected across the plates of a 220-nF capacitor. The capacitor is charged to 5.00 V, then discharged through the resistor. The time for the potential difference to decrease to 800 mV is measured by an internal clock. We have to find the range of the resistance of the resistor, if the range of discharge times that can be handled is from to 6.0 ms.

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Capacitance of the capacitor is

As equation for discharge of a capacitor in a RC circuit is

Therefore, variation of voltage across the capacitor as it discharges with time will be given by the equation

It is given that an internal clock measures time, t, for the voltage of the capacitor charged to 5.00 V to drop to 800 mV. Therefore, relation between t and the resistance R is

And

(a)

For ,

resistance in the circuit has to be

(b)

For ,

resistance in the circuit has to be

Therefore, the range of the resistance of the resistor has to be from 24.8 to 14.9 k.