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“Capacitors: Networks, Slabs and Redistribution in Depth” is available to Standard subscribers.
Beyond the textbook: bridge and symmetric networks, slabs that fill part of a gap, charge sharing and the heat lost, and a battery switched on and off. The problems that JEE, NEET and A-Level Physics ask most, with a full timed paper.
3Lessons11Problems2Python Labs1Question Set1Mock Test
Capacitor networks and symmetry: When a network is neither series nor parallel, two rules still solve it. The voltages round a loop add to zero. The charges on the plates joined at an isolated node add to the charge that node had at the start. Points at equal potential can be joined, and a capacitor between them holds no charge. A bridge, a cube of capacitors and an endless ladder then take a few lines.
Partly filled capacitors: Cut a partly filled capacitor along the field lines and the pieces are in parallel. Cut it across the field lines and the layers are in series. A level gauge, a slab over part of the plates and a slab sliding in all follow. The pull on a sliding slab is F=21V2dC/dx
, with the battery on or off. A thin air gap beside a slab takes most of the field, so it can lower the breakdown voltage.
Charge sharing, heat and work by a battery: Every change in a circuit of capacitors is an audit of energy: the work of the batteries, ∑VΔQ, equals the energy stored plus heat plus mechanical work. A capacitor that goes from V1 to V2 through any resistance loses 21C(ΔV)2 as heat. Charging in N equal steps wastes only N1 of the stored energy. A moving slab, a stack switched from parallel to series and a capacitor that ferries charge all follow from the audit.