Dielectric with Battery Connected
For complete insertion of a linear dielectric K while an ideal battery remains connected, V is fixed, C becomes KC_0, and battery exchange changes Q and U.
Why this shows up in the exam
battery-connected dielectric insertion · extra charge supplied by battery · energy change at fixed voltage
Learn the idea
With fixed voltage, inserting dielectric increases capacitance, charge, and energy. The battery keeps the electrical height difference fixed and supplies extra charge when dielectric lowers the effective field cost.
🧠 Memory hook: Battery connected means V fixed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- C = K C₀ — complete dielectric fill
- Q = CV; U = (1/2)CV² — fixed V from ideal battery
How to approach it
- 1Circle the fixed quantity V
- 2Update capacitance from geometry
- 3Recompute Q and U, including battery role if asked
Common slip-ups that cost marks
- •Conserving capacitor charge while battery is attached
- •Using U=Q squared/(2C) with old Q
- •Ignoring work exchanged with the battery
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Two point charges 1 microC and 2 microC are 1 m apart in vacuum. Take k = 9 x 10^9 SI. Find the force magnitude.
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