Question

The \({\rm{RC}}\) time constant in heart defibrillation is crucial to limiting the time the current flows. If the capacitance in the defibrillation unit is fixed, how would you manipulate resistance in the circuit to adjust the \({\rm{RC}}\) constant \(\tau \)? Would an adjustment of the applied voltage also beaded to ensure that the current delivered has an appropriate value?

Short answer

The value of \(\tau \) rises as resistance rises.

Step-by-step solution

Concept and relation 

To limit the time the current flows, in the heart defibrillator the role of the RC time constant is very important.

The relation of the time constant is given as,

\(\tau {\rm{ = RC}}\)

Here,\({\rm{R}}\)is the resistance in the circuit and\({\rm{C}}\)is the capacitance of the capacitor.

Explanation

Now according to the above equation if the capacitance is kept constant then the time constant in the circuit is only manipulated by varying the given resistance, as the time constant and the resistance both are directly proportional to each other, increasing the value for the resistance in the circuit it will lead to the increase in the time constant and decreasing its value will lead to the decrease in the value of the time constant.

If the capacitance is constant, increasing resistance raises the \(\tau \) value and vice versa.

This allows us to change the RC constant value, but keep in mind that a higher resistance requires a higher voltage to produce the same current.