Two capacitors \(C_1\) and \(C_2\) are connected in series across a battery. While deriving their effective capacitance, the plates of both capacitors are taken to carry the same charges \(\pm Q\). Which of the following gives the reason for this?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Unequal charges would leave a net charge on a capacitor and a field in the joining wire, so charge would flow.
The outer plates are joined to the battery and get charges \( +Q \) and \( -Q \). The right plate of \( C_1 \) and the left plate of \( C_2 \) form one isolated conductor with the wire between them.
Option (1) The two capacitors have equal capacitance, so the same voltage gives each of them the same charge. — Incorrect. \( C_1 \) and \( C_2 \) can be different. The charges are still equal, while the voltages \( Q/C_1 \) and \( Q/C_2 \) differ.
Option (2) The potential difference across each capacitor is equal to the emf of the battery joined to them. — Incorrect. In series the potential drops add up to the battery voltage, \( V=V_1+V_2 \). Equal voltage on each belongs to a parallel combination.
Option (3) The battery pushes the same charge Q onto every plate, including the two inner plates joined by the wire. — Incorrect. The inner plates get \( -Q \) and \( +Q \) by separation of charge in the joined conductor. Their total charge stays zero.
Option (4) Unequal charges would leave a net charge on a capacitor and a field in the joining wire, so charge would flow. — Correct. Charge flows in the wire until each capacitor has zero net charge and the wire has no field. So the plates of both capacitors carry \( \pm Q \).
NCERT (2026-27):
Capacitors in series – “… It then follows that the right plate of C1 has charge –Q and the left plate of C2 has charge Q. If this was not so, the net charge on each capacitor would not be zero. This would result in an electric field in the conductor connecting C1 and C2. Charge would flow until the net charge on both C1 and C2 is zero and there is no electric field in the conductor connecting C1 and C2. Thus, in the series combination, charges on the two plates (±Q) are the same on each capacitor.”