Two capacitors of capacitance of \( 6\,\mu\mathrm{F} \) and \( 12\,\mu\mathrm{F} \) are connected in series with a battery. The voltage across \( 6\,\mu\mathrm{F} \) capacitor is 2 V. The total voltage across the combination is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3 V
Capacitors in series carry the same charge, and the total voltage is the sum of the voltages across them.
\( \displaystyle Q = C_1 V_1 = 6\,\mu\mathrm{F} \times 2\,\mathrm{V} = 12\,\mu\mathrm{C} \)
\( \displaystyle V_2 = \frac{Q}{C_2} = \frac{12\,\mu\mathrm{C}}{12\,\mu\mathrm{F}} = 1\,\mathrm{V} \)
\( \displaystyle V = V_1 + V_2 = 2\,\mathrm{V} + 1\,\mathrm{V} = 3\,\mathrm{V} \)