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At t = 0 a switch is closed in a circuit containing a cell, resistors R and R', an inductor L, and a capacitor C. The current through the cell is found to be independent of time from the moment the switch is closed. What are the conditions on R' and R?

1. R' = 2R and R = sqrt(L / (2C))
2. R' = 2R and R = sqrt(L / C)
3. R' = R and R = sqrt(L / (2C))
4. R' = R and R = sqrt(L / C)

Correct answer: R' = 2R and R = sqrt(L / (2C))

Solution

For current through the cell to be time-independent, the circuit must be critically configured so that inductive and capacitive transients cancel. The standard result for this configuration is R' = 2R and R = sqrt(L/(2C)), ensuring the effective impedance seen by the cell is purely resistive and constant.

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