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A 2 μF capacitor is connected to a 50 V supply and a 3 μF capacitor is connected to a 100 V supply. Now, after removing the batteries, the plates having the same type of charge are joined together to form a new capacitor. The potential difference across it is ______ V.

Asked in GUJCET 2020 · Redistribution of charge

• (1) 20
• (2) 333
• (3) 80
• (4) 75

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 20 V. Sanity check: joining unlike plates would give (300 - 100)/5 = 40 V, and joining like plates gives a common voltage between 50 V and 100 V.
• (2) This divides the total charge by the series capacitance, (2×3)/(2+3) = 1.2 μF: (400)/(1.2) = 333 V. Joined plate to plate, the capacitors are in parallel (5 μF).
• (4) This is the plain average of 50 V and 100 V. The common voltage is weighted by capacitance, so the larger 3 μF pulls it towards 100 V.

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