Review Question

1. Review Question Describe what happens to the lightbulb after the switch is closed. Assume that the capacitor has large capacitance and is initially uncharged, and assume that the lightbulb illuminates when connected directly across the battery terminals.

2. Charging a Capacitor in an RC circuit • As charge builds up on the plates of the capacitor, the voltage across the capacitor increases and the current flowing decreases. • The rate of charging decreases as the plates of the capacitor begin to fill up with charge. • Where V(t) is the potential difference across the capacitor • V0 is the supply voltage • t is the time elapsed since charging began • τ (tau) is the time taken for the voltage to increase to 0.63 of the supply voltage. It can be found by using the equation • Where R is the resistance in the circuit and C is the capacitance in the circuit.

3. Charging a Capacitor V(t) • After τseconds, the capacitor will have reached 63% of its full amount of charge. • Thus, the charging time can be increased by increasing the resistance or by increasing the capacitance. • τ is called the time constant and is given by the equation: V0 0.63V0 Where R is the resistance in the circuit and C is the capacitance.

4. Current in a Charging Capacitor • As the voltage across the capacitor increases, it becomes more difficult for charge to flow. • Thus the current will be maximum at the start of charging, and will be zero when the capacitor is charged to the supply voltage.

5. Discharging a Capacitor • As a capacitor is discharged through a resistor, the voltage across it drops. • The current flowing will be high initially (as the voltage is initially large), but will gradually slow. • The voltage across the capacitor will decrease as the plates lose their charge. V0 0.37V0

6. Capacitors Review Conceptual Quiz: Explaining Capacitors

7. Conceptual Quiz: Capacitors • The plates of a capacitor are connected to a battery. What happens to the charge on the plates if the connecting wires are removed from the battery? What happens to the charge if the wires are removed from the battery and connected to each other? • A farad is a very large unit of capacitance. Calculate the length of one side of a square, air-filled capacitor that has a capacitance of 1 F and a plate separation of 1 m • A pair of capacitors are connected in parallel while an identical pair are connected in series. Which pair would be more dangerous to handle after being connected to the same battery? Explain. • If you are given three different capacitors C1, C2 and C3, how many different combinations of capacitance can you produce?

8. Capacitors -- Concepts • The sum of the charges on both plates of a capacitor is zero. What does a capacitor store? • Because the charges on the plates of a parallel-plate capacitor are opposite in sign, they attract each other. Hence, it would take positive work to increase the plate separation. What type of energy in the system changes due to the external work done in this process? • Explain why the work needed to move a charge Q through a potential difference V is W = QV whereas the energy stored in a charged capacitor is Ep = ½Q V. • If the potential difference across a capacitor is doubled, by what factor does the energy stored change? • If you were asked to design a capacitor where small size and large capacitance were required, what factors would be important in your design?