he timing device in an automobile's intermittent wiper system is based on an RC time constant and utilizes a 0.500-μF capacitor and a variable resistor. Over what range must R be made to vary to achieve time constants from 2.00 to 15.0 s?

4000k-ohm to 10,000k-ohm

Explanation:

As we know that time constant for an RC circuit is t=RC

Putting the values of t we can get the range of varaiable resistor as;

t=RC

Putting t=2 we get the first value of the range for the variable resistor

2=R*0.500*10^-6

R=2 / (0.500*10^-6)

R=4*10^6

R=4000k-ohm

Now putting t=5 we get the final value for the range of variable resistor

t=RC

5=R*0.500*10^-6

R=5 / (0.500*10^-6)

R=10*10^6

R=10,000k-ohm

So variable resistance must be made to vary in the range from 4000k-ohm to 10,000k-ohm