A battery with potential V across it is connected to a combination of two identical resistors, and then has current i through it. What are the potential difference across and the current through either resistor if the resistors are connected in series?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{V}{2},\ i \)
In a series connection the same current flows through every resistor, and it is the current that the battery supplies, i. The potential difference V of the battery divides among the resistors in proportion to their resistances, so two identical resistors share it equally.
\( R_{\mathrm{eq}} = R + R = 2R,\qquad i = \displaystyle\frac{V}{2R} \)
\( \displaystyle V_1 = V_2 = iR = \frac{V}{2R}\times R = \frac{V}{2} \)
Each resistor therefore has a potential difference \( V/2 \) across it and carries the current i.