For school, I was trying to solve a question that features a circuit with a resistor, an inductor, and a battery all connected in series. It then shows an increasing concave down graph of something vs. t – the graph started at the origin and had a horizontal asymptote at some positive value of x. The "something" could be:
A. The potential difference across the resistor
B. The potential difference across the inductor
and/or C. The current in the circuit.
I had reasoned that it would be all 3, because when an inductor is first connected to a battery at time t=0, it doesn't allow electricity to flow, but as time goes on, it allows more and more electricity to flow until it is essentially acting like a wire. Therefore, current will increase, and voltage will also increase across the entire circuit. However, when this problem was graded, it turned out that B was incorrect, and I was not told why. Why is this the case?
Best Answer
It's not clear exactly what you mean by "across the entire circuit", but think about your model of a battery.
For a simple analysis that is usually used for circuits like this, the battery is considered as a constant voltage source. Therefore, by Kirchoff's Voltage Law,
$$V_b = V_l + V_r$$
where $V_b$, $V_l$ and $V_r$ are the voltages across the battery, the inductor, and the resistor respectively (and when you choose the same sign convention I did for each of them, but since you didn't bother to include a circuit diagram in your question, I don't feel obligated to provide one to indicate the sign conventions in my answer).
So if the voltage across the resistor increases, the voltage across the inductor must decrease.