Explain why the voltage across a capacitor cannot change instantaneously
Answers
When we close the switch at time = 0, the voltage on the initially uncharged capacitor increases. With an ideal capacitor, the final voltage is equal to the battery voltage. The “rise time” is a function of the capacitor size and the value of the resistor. Energy from the battery is transfered to the capacitor. We say that work is done in this process. Our universe does not allow infinite changes in energy because there is a limit to the rate at which work an be done. FUN FACT: All real circuits have resistance. Even if we connect a capacitor directly to the battery, we still have resistance. This hidden resistance is known as “battery internal resistance” and capacitor “equivalent series resistance.” Since there is always resistance, there will always be a limit to the amount of current that can flow in this circuit. This imposes a limit on the time it takes to transfer energy from the battery to the capacitor. Yes, the resistor changes some of the battery’s energy to heat See attached file The same energy discussion applies. When the switch closes at time = 0 there is no energy stored in the inductor. Recall that the inductor stores energy as a magnetic field. This field is proportional to the amount of current that flows in the inductor. This is where things get interesting. Since it takes time for the battery to “charge” the inductor, there must be a way to keep the inductor energy zero when the switch is closed at t = 0. This demands an inductor current of zero when the switch closes. Consequently, the voltage as measured across the inductor instantaneously jump to the battery voltage when the switch is closed! Fun Fact: The electronic fuel injector in a diesel engine contains a magnetically activated plunger. This device appears as an inductor when you try to activate the injector. The inductors tendency to initially “jump” to the applied voltage limits the injectors turn on speed.