10.5 RC Circuits

When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the RC constant of the circuit—it is not possible to measure time variations shorter than RC. How would you manipulate R and C in the circuit to allow the necessary measurements?

The timing device in an automobile’s intermittent wiper system is based on an RC time constant and utilizes a $0.500 - \mu \text{F}$ 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?

The duration of a photographic flash is related to an RC time constant, which is $0.100 \mu \text{s}$ for a certain camera. (a) If the resistance of the flash lamp is $0.0400 \Omega$ during discharge, what is the size of the capacitor supplying its energy? (b) What is the time constant for charging the capacitor, if the charging resistance is $800 \text{k} \Omega$?

A $500 - \Omega$ resistor, an uncharged $1.50 - \mu \text{F}$ capacitor, and a 6.16-V emf are connected in series. (a) What is the initial current? (b) What is the RC time constant? (c) What is the current after one time constant? (d) What is the voltage on the capacitor after one time constant?

An ECG monitor must have an RC time constant less than $1.00 \times 10^{2} \mu \text{s}$ to be able to measure variations in voltage over small time intervals. (a) If the resistance of the circuit (due mostly to that of the patient’s chest) is $1.00 \text{k} \Omega$, what is the maximum capacitance of the circuit? (b) Would it be difficult in practice to limit the capacitance to less than the value found in (a)?

If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an RC discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one RC constant is acceptable, and given that the flash is driven by a $600 - \mu \text{F}$ capacitor, what is the resistance in the flash tube?