An ECG monitor must have an RC time constant less than 1.00 times 10 to the two microseconds to be able to measure variations in voltage over small time intervals. If the resistance of the circuit due mostly to that of the patient’s chest is 1.00 kiloohms, what is the maximum capacitance of the circuit?
We’ll call the given time constant, 1.00 times 10 to the two microseconds, 𝜏. We’re told that the circuit’s resistance is 1.00 kiloohms, what we’ll call capital 𝑅. We want to solve for the maximum capacitance allowable in this circuit. We’ll name that 𝐶.
To solve for that capacitance, let’s recall the equation for a time constant in an RC circuit. In this type of circuit, 𝜏, the time constant, is equal to the product of the resistance and the capacitance. In our scenario, we’ve been given 𝜏 and 𝑅 and want to solve for 𝐶.
We rearrange our equation and find that 𝐶 is equal to 𝜏 divided by 𝑅. When we plug in values for 𝜏 and 𝑅, being careful to use units of seconds for our time constant and units of ohms for our resistance, when we calculate this fraction, we find that 𝐶 is equal to 1.00 times 10 to the negative seventh farads. That’s the maximum capacitance of the circuit.