# Video: Calculating the Time Constant of an RC Circuit

The timing device in an automobileโs intermittent wiper system is based on an RC time constant and utilizes a 0.500-๐F capacitor and a variable resistor. Over what range must ๐ be made to vary to achieve time constants from 2.00 to 15.0 s?

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### Video Transcript

The timing device in an automobileโs intermittent wiper system is based on an RC time constant and utilizes a 0.500-microfarad capacitor and a variable resistor. Over what range must ๐ be made to vary to achieve time constants from 2.00 to 15.0 seconds?

We can call the 0.500-microfarad capacitor ๐ถ. And we want to solve for the range of ๐, the resistance. Weโll call the lower end of that range ๐ sub one and the upper end ๐ sub two that must be made so that the total time constants of our circuit vary from 2.00 to 15.0 seconds.

Weโll call the lower end of that 2.00 seconds ๐ก sub one and the upper end weโll call ๐ก sub two. And RC time constant ๐ก is simply the product of the resistance times the capacitance in a circuit. So we can write that ๐ก one equals ๐ one times ๐ถ and ๐ก two equals ๐ two times ๐ถ.

Rearranging these equations to solve for the resistances, ๐ one is ๐ก one over ๐ถ and ๐ two is ๐ก two over ๐ถ. Weโre giving the capacitance ๐ถ as well as the time range in our problem statement. So weโre ready to plug in and solve for the range of ๐.

When we do and calculate these two fractions, we find that to three significant figures ๐ one is 4.00 million ohms and ๐ two is 30.0 million ohms. This is the lower and upper end of the range over which our resistor must vary.