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œ‡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.

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