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?

$\frac{V}{2},i$

The correct answer is Option (3) → $\frac{V}{2},i$

In a series combination of two identical resistors, the resistors are connected end to end.

$R_{eq}=R+R$

$R_{eq}=2R$

Now,

$I=\frac{V}{R_{eq}}=\frac{V}{2R}$ [According to Ohm's law]

$∴V=IR$ [According to Ohm's law]

$V_1=R×\frac{V}{2R}=\frac{V}{2}$

$V_2=R×\frac{V}{2R}=\frac{V}{2}$