A resistor R = 5 Ω and a coil (winding resistance negligible) are connected in series to a 10 V DC source, and the switch is closed. Which pair gives the current immediately after closing the switch and after a long time?

Answer: C. Immediately: 0 A; after a long time: 2 A

Because v = L di/dt, the current in a coil cannot change suddenly, so immediately after the switch closes the current is 0; the coil behaves like an open circuit, with the full 10 V across it. After a long time the current stops changing, the coil voltage becomes 0 (like a short circuit) and the current is 10 V/5 Ω = 2 A. In between, the current rises exponentially with time constant L/R.

• A. Starting at 2 A and falling to 0 A is what happens with a capacitor in series instead of the coil.
• B. 2 A from the start would be the case with no coil (resistor only).
• C. Correct. The coil current cannot change suddenly, so it rises from 0 A toward 2 A.