Question

You are working in a lab where RC circuits are used to delay the initiation of a process. One particular experiment involves an RC circuit with a half-life of t_1/2 = 3.00 s.Your supervisor is concerned that the initiation of the process is occurring too soon and that the half-life needs to be extended. He asks you to change the resistance of the circuit to make the half-life longer. All you can find in the supply room is a single 58.0 Ω resistor. You look at the RC circuit and see that the resistance is 55.0 Ω. You combine the new resistor with the old to extend the half-life of the circuit. Determine the new half-life (in s).

Answer 1

The half-life of the RC circuit is given by

where

........................(1)

Given

The resistance already in the circuit is 55 ohms and to extend the half-life we added a new resistor of 58 ohms in the series. The net resistance is 55 +58 = 113 ohms. Now the new half-life is

..................................(2)

dividing the equation (2) by the equation (1) we get

Putting the values

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