Two parallel plate capacitors of capacitances 2 µF and 3 µF are joined in series and the combination is connected to a battery of V volts. The values of potential across the two capacitors $V_1$ and $V_2$ and energy stored in the two capacitors $U_1$ and $U_2$ respectively are related as ________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 1
$ V_1 = \frac{C_2 V}{C_1 + C_2} = \frac{3V}{5}$
$ V_2 = \frac{C_1 V}{C_1 + C_2} = \frac{2V}{5}$
$\Rightarrow \frac{V_1}{V_2} = \frac{3}{2}$
$ U_1 = \frac {q^2}{2C_1}, U_2 = \frac{q^2}{2C_2} \Rightarrow \frac{U_1}{U_2} = \frac{C_2}{C_1} = \frac{3}{2}$
The correct answer is Option (1) → $\frac{V_1}{V_2}=\frac{U_1}{U_2}=\frac{3}{2}$