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In an RC circuit a capacitor C is charged through a resistor by an EMF source E, and in a separate RL circuit an inductor L carries current driven by the same EMF E through resistance R. Both switches are closed at t = 0. Which statement is correct?

1. The charge on C just after t = 0 is EC.
2. The charge on C long after t = 0 is EC.
3. The current in L just after t = 0 is E/R.
4. The current in L long after t = 0 is zero.

Correct answer: The charge on C long after t = 0 is EC.

Solution

Immediately after closing (t = 0+), an uncharged capacitor behaves like a short, so its charge is 0, not EC. After a long time the capacitor is fully charged to the source EMF E, giving Q = C*E = EC. An inductor opposes sudden current change, so the current in L just after t = 0 is 0 (not E/R), and long after t = 0 the inductor behaves like a wire so the steady current is E/R (not zero). Only the statement that the charge on C long after t = 0 is EC is correct.

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