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) → $\frac{V}{2},i$
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]
$V_1=R×\frac{V}{2R}=\frac{V}{2}$
$V_2=R×\frac{V}{2R}=\frac{V}{2}$