Question

The timing device in an automobile’s intermittent wiper system is based on an RC circuit and utilizes a 0.500 micro-ferade capacitor and a variable resistor. A) what would be the minimum value that R must be made to achieve time constants which vary from 2.00 to 15.0 seconds in Miliohms? B) what would be the maximum value that R must be made to achieve time constants varying from 2.00 to 15.00 In miliohms?

Answer 1

Please check the underlined part in the solution

We know that time constant in RC circuit is given by:

= R*C

R = /C

Now given that C = 0.500 micro-farad = 0.500*10^-6 F

Part A.

minimum value of R will be when time constant is minimum, So

_min = 2.00 sec

Which will give:

R_min = _min/C

R_min = 2.00/(0.500*10^-6)

R_min = 4.0*10^6 ohm

R_min = 4.0 M-ohm

(I think you need final answer Mega ohms unit and not in miliohms If you need them in miliohm, then R = 4.0*10^6*10^3*10^-3 ohm = 4.0*10^9 miliohms)

Part B.

maximum value of R will be when time constant is maximum, So

_max = 15.00 sec

Which will give:

R_max = _max/C

R_max = 15.00/(0.500*10^-6)

R_max = 30.0*10^6 ohm

R_max = 30.0 M-ohm

(I think you need final answer Mega ohms unit and not in miliohms If you need them in miliohm, then R = 30.0*10^6*10^3*10^-3 ohm = 30.0*10^9 miliohms)

Let me know if you've any query.