After getting everything wrong last time, Bob now asks for help when he\'s confu

Question

After getting everything wrong last time, Bob now asks for help when he's confused. Help him become less confused by answering his questions below. a) "I don't understand how light bulbs can come on instantly after you flick the switch. Doesn't it take at least a second or two for the electrons to travel from the wall all the way up the wire into the light bulb?" b) "I have two equations for electrical power: P = I^2R and P = V^2/R. The first one makes it look like increasing resistance R will increase my electrical power, but the second one says that increasing R makes power decrease. One of them must be right: if I replace a 10 Ohm resistor in a circuit with 20 Ohm resistor, will the power going to that resistor increase or decrease? c) "I need a 6 mu F capacitor for a cool circuit I'm making. Can't I just connect a 2 mu F and 4 mu F in series?" d)"Speaking of capacitors, since C = Q/V, that means if Q = 0, then C = 0 too, right? e) "Why are there at least two prongs on every electrical plug? If power is traveling in one direction (from the wall to the appliance), why can't there be just one wire carrying it? And don't just say "because circuits need to be closed' - after all, current can flow through a capacitor, and that's an open circuit. f) "I have a great idea that should make me filthy rich. I'm going to build a generator with a huge number of loops and an enormous magnetic field, but also with very low friction materials. That way, the opposing force against the spinning loops will be negligible. Therefore due to inertia, the loops will spin forever, with only very minimal input power to overcome the tiny amount of friction. In other words, I have found a loophole in conservation of energy: more electric power will be output than the mechanical power that was input. Who can stop me?!"

Explanation / Answer

a) When the switch is closed, electrons flow into the wire where they collide with the electrons already in the wire and push them along. The voltage travels along the wire at somewhere between a tenth and a half of the speed of light depending on the type of wire, and reaches the light bulb in a few nanoseconds. That's how the electrons in the bulb filament start moving within a few nanoseconds after closing the switch.

b) Using ohm's law, depending on the increment or decrement of resistor, the power can increase or decrease. As, change in resistor also leds to change in current and voltage, the final value depends on that.

c) No, capacitors can't be joined in series to get an equivalent capacitance that is equal to their sum. The capacitors are inversely proportional to voltage, hence to get 6uF capacitor, one hs to connect them in parallel.

d) The charge q denotes the charge that the capacitor is able to store. So, if Q=0, it does not implies that C will also be zero.

e) The circuit needs to be closed. In a Capacitor, the circuit is not open a current known as displacement current exists between the plates of capacitor which due to electric field beetween the plates.

f) The eddy currents produced in the circuit due to movement of coil and changing magnetic field will oppose the power output thus restoring energy conservation.

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